M0160 Optimization

Faculty of Science
Spring 2025
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
In-person direct teaching
Teacher(s)
doc. Mgr. Petr Zemánek, Ph.D. (lecturer)
Guaranteed by
doc. Mgr. Petr Zemánek, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
After this course the studnets get knowledge and skill concerning basic methods of solutions of some optimization problems.
Learning outcomes
At the end of this course the students will be able to solve problems of the linear, integer, quadratic, and dynamic programming as well as basic problems of calculus of variations.
Syllabus
  • I. Linear programming.
  • Ia. Integer programming.
  • II. Quadratic programming.
  • III. Dynamic programming: Bellman optimization principle, finite deterministic and stochastic decision models, infinite steps models.
  • IV. Elements of the calculus of variations and discrete optimization: historical motivation, Euler-Lagrange equation and the first variation, second variation, elementary difference equations and recurrence relations, discrete calculus of variations.
Literature
    recommended literature
  • DOŠLÝ, Ondřej. Základy konvexní analýzy a optimalizace v R^n (Elements of convex analysis and optimization in R^n). 1st ed. Brno: Masarykova univerzita, 2005, 194 pp. ISBN 80-210-3905-1. info
  • DANTZIG, George Bernard and Mukund Narain THAPA. Linear programming. New York: Springer, 2003, xxv, 448 s. ISBN 0-387-98613-8. info
  • BAZARAA, Mokhtar S., John J. JARVIS and Hanif D. SHERALI. Linear programming and network flows. 2nd ed. New York: John Wiley & Sons, Inc., 1990, xiv+684 pp. ISBN 0-471-63681-9. info
  • KÜNZI, Hans P., Wilhelm KRELLE and Werner OETTLI. Nichtlineare Programmierung. Berlin: Springer-Verlag, 1962, 221 s. info
  • HAMALA, Milan. Nelineárne programovanie. 2. dopl. vyd. Bratislava: Alfa, vydavateľstvo technickej a ekonomickej literatúry, 1972, 240 s. info
  • KAUMAN, A. and R CRUON. Dynamické programovanie. Bratislavaa, 1969, 312 pp. Matematické metódy v ekonomike, Alfa. ISBN 302 - 063 - 69. info
  • NEMHAUSER, George, L. Introduction to Dynamic Programming. New York: John Wiley, 1966, 350 pp. ISBN 0-8247-8245-3. info
  • BELLMAN, Richard. Dynamic programming. Dover ed. Mineola, N.Y.: Dover Publications, 2003, xxv, 340. ISBN 0486428095. info
  • GEL'FAND, Izrail Moisejevič and Sergej Vasil'jevič FOMIN. Calculus of variations. Edited by Richard A. Silverman. Mineola, N. Y.: Dover Publications, 2000, vii, 232 s. ISBN 0-486-41448-5. info
  • ŠKRÁŠEK, Josef and Zdeněk TICHÝ. Základy aplikované matematiky. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1990, 853 s. ISBN 80-03-00111-0. info
Teaching methods
Lectures and exercises.
Assessment methods
The exam has both written and oral components. In the written part students solve particular examples. In the oral part a question concerning one of the topic I-IV (see the syllabus above) is given and the knowledge of basic concepts is required.

The conditions (especially regarding the form of the tests and exam) will be specified according to the epidemiological situation and valid restrictions.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is taught: every week.
Teacher's information
The lessons are usually in Czech or in English as needed, and the relevant terminology is always given with English equivalents. The target skills of the study include the ability to use the English language passively and actively in their own expertise and also in potential areas of application of mathematics. Assessment in all cases may be in Czech and English, at the student's choice.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024.

M0160 Optimization

Faculty of Science
Spring 2024
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
doc. Mgr. Petr Zemánek, Ph.D. (lecturer)
Guaranteed by
doc. Mgr. Petr Zemánek, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 19. 2. to Sun 26. 5. Tue 10:00–11:50 M1,01017
  • Timetable of Seminar Groups:
M0160/01: Mon 19. 2. to Sun 26. 5. Fri 12:00–13:50 M1,01017, P. Zemánek
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
After this course the studnets get knowledge and skill concerning basic methods of solutions of some optimization problems.
Learning outcomes
At the end of this course the students will be able to solve problems of the linear, integer, quadratic, and dynamic programming as well as basic problems of calculus of variations.
Syllabus
  • I. Linear programming.
  • Ia. Integer programming.
  • II. Quadratic programming.
  • III. Dynamic programming: Bellman optimization principle, finite deterministic and stochastic decision models, infinite steps models.
  • IV. Elements of the calculus of variations and discrete optimization: historical motivation, Euler-Lagrange equation and the first variation, second variation, elementary difference equations and recurrence relations, discrete calculus of variations.
Literature
    recommended literature
  • DOŠLÝ, Ondřej. Základy konvexní analýzy a optimalizace v R^n (Elements of convex analysis and optimization in R^n). 1st ed. Brno: Masarykova univerzita, 2005, 194 pp. ISBN 80-210-3905-1. info
  • DANTZIG, George Bernard and Mukund Narain THAPA. Linear programming. New York: Springer, 2003, xxv, 448 s. ISBN 0-387-98613-8. info
  • BAZARAA, Mokhtar S., John J. JARVIS and Hanif D. SHERALI. Linear programming and network flows. 2nd ed. New York: John Wiley & Sons, Inc., 1990, xiv+684 pp. ISBN 0-471-63681-9. info
  • KÜNZI, Hans P., Wilhelm KRELLE and Werner OETTLI. Nichtlineare Programmierung. Berlin: Springer-Verlag, 1962, 221 s. info
  • HAMALA, Milan. Nelineárne programovanie. 2. dopl. vyd. Bratislava: Alfa, vydavateľstvo technickej a ekonomickej literatúry, 1972, 240 s. info
  • KAUMAN, A. and R CRUON. Dynamické programovanie. Bratislavaa, 1969, 312 pp. Matematické metódy v ekonomike, Alfa. ISBN 302 - 063 - 69. info
  • NEMHAUSER, George, L. Introduction to Dynamic Programming. New York: John Wiley, 1966, 350 pp. ISBN 0-8247-8245-3. info
  • BELLMAN, Richard. Dynamic programming. Dover ed. Mineola, N.Y.: Dover Publications, 2003, xxv, 340. ISBN 0486428095. info
  • GEL'FAND, Izrail Moisejevič and Sergej Vasil'jevič FOMIN. Calculus of variations. Edited by Richard A. Silverman. Mineola, N. Y.: Dover Publications, 2000, vii, 232 s. ISBN 0-486-41448-5. info
  • ŠKRÁŠEK, Josef and Zdeněk TICHÝ. Základy aplikované matematiky. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1990, 853 s. ISBN 80-03-00111-0. info
Teaching methods
Lectures and exercises.
Assessment methods
The exam has both written and oral components. In the written part students solve particular examples. In the oral part a question concerning one of the topic I-IV (see the syllabus above) is given and the knowledge of basic concepts is required.

The conditions (especially regarding the form of the tests and exam) will be specified according to the epidemiological situation and valid restrictions.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Teacher's information
The lessons are usually in Czech or in English as needed, and the relevant terminology is always given with English equivalents. The target skills of the study include the ability to use the English language passively and actively in their own expertise and also in potential areas of application of mathematics. Assessment in all cases may be in Czech and English, at the student's choice.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2025.

M0160 Optimization

Faculty of Science
Spring 2023
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
doc. Mgr. Petr Zemánek, Ph.D. (lecturer)
Guaranteed by
doc. Mgr. Petr Zemánek, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Wed 12:00–13:50 M1,01017
  • Timetable of Seminar Groups:
M0160/01: Fri 12:00–13:50 M2,01021, P. Zemánek
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
After this course the studnets get knowledge and skill concerning basic methods of solutions of some optimization problems.
Learning outcomes
At the end of this course the students will be able to solve problems of the linear, integer, quadratic, and dynamic programming as well as basic problems of calculus of variations.
Syllabus
  • I. Linear programming.
  • Ia. Integer programming.
  • II. Quadratic programming.
  • III. Dynamic programming: Bellman optimization principle, finite deterministic and stochastic decision models, infinite steps models.
  • IV. Elements of the calculus of variations and discrete optimization: historical motivation, Euler-Lagrange equation and the first variation, second variation, elementary difference equations and recurrence relations, discrete calculus of variations.
Literature
    recommended literature
  • DOŠLÝ, Ondřej. Základy konvexní analýzy a optimalizace v R^n (Elements of convex analysis and optimization in R^n). 1st ed. Brno: Masarykova univerzita, 2005, 194 pp. ISBN 80-210-3905-1. info
  • DANTZIG, George Bernard and Mukund Narain THAPA. Linear programming. New York: Springer, 2003, xxv, 448 s. ISBN 0-387-98613-8. info
  • BAZARAA, Mokhtar S., John J. JARVIS and Hanif D. SHERALI. Linear programming and network flows. 2nd ed. New York: John Wiley & Sons, Inc., 1990, xiv+684 pp. ISBN 0-471-63681-9. info
  • KÜNZI, Hans P., Wilhelm KRELLE and Werner OETTLI. Nichtlineare Programmierung. Berlin: Springer-Verlag, 1962, 221 s. info
  • HAMALA, Milan. Nelineárne programovanie. 2. dopl. vyd. Bratislava: Alfa, vydavateľstvo technickej a ekonomickej literatúry, 1972, 240 s. info
  • KAUMAN, A. and R CRUON. Dynamické programovanie. Bratislavaa, 1969, 312 pp. Matematické metódy v ekonomike, Alfa. ISBN 302 - 063 - 69. info
  • NEMHAUSER, George, L. Introduction to Dynamic Programming. New York: John Wiley, 1966, 350 pp. ISBN 0-8247-8245-3. info
  • BELLMAN, Richard. Dynamic programming. Dover ed. Mineola, N.Y.: Dover Publications, 2003, xxv, 340. ISBN 0486428095. info
  • GEL'FAND, Izrail Moisejevič and Sergej Vasil'jevič FOMIN. Calculus of variations. Edited by Richard A. Silverman. Mineola, N. Y.: Dover Publications, 2000, vii, 232 s. ISBN 0-486-41448-5. info
  • ŠKRÁŠEK, Josef and Zdeněk TICHÝ. Základy aplikované matematiky. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1990, 853 s. ISBN 80-03-00111-0. info
Teaching methods
Lectures and exercises.
Assessment methods
The exam has both written and oral components. In the written part students solve particular examples. In the oral part a question concerning one of the topic I-IV (see the syllabus above) is given and the knowledge of basic concepts is required.

The conditions (especially regarding the form of the tests and exam) will be specified according to the epidemiological situation and valid restrictions.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Teacher's information
The lessons are usually in Czech or in English as needed, and the relevant terminology is always given with English equivalents. The target skills of the study include the ability to use the English language passively and actively in their own expertise and also in potential areas of application of mathematics. Assessment in all cases may be in Czech and English, at the student's choice.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2024, Spring 2025.

M0160 Optimization

Faculty of Science
Spring 2022
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
doc. Mgr. Petr Zemánek, Ph.D. (lecturer)
Guaranteed by
doc. Mgr. Petr Zemánek, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Fri 10:00–11:50 M2,01021
  • Timetable of Seminar Groups:
M0160/01: Fri 12:00–13:50 M2,01021, P. Zemánek
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
After this course the studnets get knowledge and skill concerning basic methods of solutions of some optimization problems.
Learning outcomes
At the end of this course the students will be able to solve problems of the linear, integer, quadratic, and dynamic programming as well as basic problems of calculus of variations.
Syllabus
  • I. Linear programming.
  • Ia. Integer programming.
  • II. Quadratic programming.
  • III. Dynamic programming: Bellman optimization principle, finite deterministic and stochastic decision models, infinite steps models.
  • IV. Elements of the calculus of variations and discrete optimization: historical motivation, Euler-Lagrange equation and the first variation, second variation, elementary difference equations and recurrence relations, discrete calculus of variations.
Literature
    recommended literature
  • DOŠLÝ, Ondřej. Základy konvexní analýzy a optimalizace v R^n (Elements of convex analysis and optimization in R^n). 1st ed. Brno: Masarykova univerzita, 2005, 194 pp. ISBN 80-210-3905-1. info
  • DANTZIG, George Bernard and Mukund Narain THAPA. Linear programming. New York: Springer, 2003, xxv, 448 s. ISBN 0-387-98613-8. info
  • BAZARAA, Mokhtar S., John J. JARVIS and Hanif D. SHERALI. Linear programming and network flows. 2nd ed. New York: John Wiley & Sons, Inc., 1990, xiv+684 pp. ISBN 0-471-63681-9. info
  • KÜNZI, Hans P., Wilhelm KRELLE and Werner OETTLI. Nichtlineare Programmierung. Berlin: Springer-Verlag, 1962, 221 s. info
  • HAMALA, Milan. Nelineárne programovanie. 2. dopl. vyd. Bratislava: Alfa, vydavateľstvo technickej a ekonomickej literatúry, 1972, 240 s. info
  • KAUMAN, A. and R CRUON. Dynamické programovanie. Bratislavaa, 1969, 312 pp. Matematické metódy v ekonomike, Alfa. ISBN 302 - 063 - 69. info
  • NEMHAUSER, George, L. Introduction to Dynamic Programming. New York: John Wiley, 1966, 350 pp. ISBN 0-8247-8245-3. info
  • BELLMAN, Richard. Dynamic programming. Dover ed. Mineola, N.Y.: Dover Publications, 2003, xxv, 340. ISBN 0486428095. info
  • GEL'FAND, Izrail Moisejevič and Sergej Vasil'jevič FOMIN. Calculus of variations. Edited by Richard A. Silverman. Mineola, N. Y.: Dover Publications, 2000, vii, 232 s. ISBN 0-486-41448-5. info
  • ŠKRÁŠEK, Josef and Zdeněk TICHÝ. Základy aplikované matematiky. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1990, 853 s. ISBN 80-03-00111-0. info
Teaching methods
Lectures and exercises.
Assessment methods
The exam has both written and oral components. In the written part students solve particular examples. In the oral part a question concerning one of the topic I-IV (see the syllabus above) is given and the knowledge of basic concepts is required.

The conditions (especially regarding the form of the tests and exam) will be specified according to the epidemiological situation and valid restrictions.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Teacher's information
The lessons are usually in Czech or in English as needed, and the relevant terminology is always given with English equivalents. The target skills of the study include the ability to use the English language passively and actively in their own expertise and also in potential areas of application of mathematics. Assessment in all cases may be in Czech and English, at the student's choice.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2023, Spring 2024, Spring 2025.

M0160 Optimization

Faculty of Science
Spring 2021
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
doc. Mgr. Petr Zemánek, Ph.D. (lecturer)
Guaranteed by
doc. Mgr. Petr Zemánek, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 1. 3. to Fri 14. 5. Fri 10:00–11:50 M1,01017
  • Timetable of Seminar Groups:
M0160/01: Mon 1. 3. to Fri 14. 5. Fri 12:00–13:50 M1,01017, P. Zemánek
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
After this course the studnets get knowledge and skill concerning basic methods of solutions of some optimization problems.
Learning outcomes
At the end of this course the students will be able to solve problems of the linear, integer, quadratic, and dynamic programming as well as basic problems of calculus of variations.
Syllabus
  • I. Linear programming.
  • Ia. Integer programming.
  • II. Quadratic programming.
  • III. Dynamic programming: Bellman optimization principle, finite deterministic and stochastic decision models, infinite steps models.
  • IV. Elements of the calculus of variations and discrete optimization: historical motivation, Euler-Lagrange equation and the first variation, second variation, elementary difference equations and recurrence relations, discrete calculus of variations.
Literature
    recommended literature
  • DOŠLÝ, Ondřej. Základy konvexní analýzy a optimalizace v R^n (Elements of convex analysis and optimization in R^n). 1st ed. Brno: Masarykova univerzita, 2005, 194 pp. ISBN 80-210-3905-1. info
  • DANTZIG, George Bernard and Mukund Narain THAPA. Linear programming. New York: Springer, 2003, xxv, 448 s. ISBN 0-387-98613-8. info
  • BAZARAA, Mokhtar S., John J. JARVIS and Hanif D. SHERALI. Linear programming and network flows. 2nd ed. New York: John Wiley & Sons, Inc., 1990, xiv+684 pp. ISBN 0-471-63681-9. info
  • KÜNZI, Hans P., Wilhelm KRELLE and Werner OETTLI. Nichtlineare Programmierung. Berlin: Springer-Verlag, 1962, 221 s. info
  • HAMALA, Milan. Nelineárne programovanie. 2. dopl. vyd. Bratislava: Alfa, vydavateľstvo technickej a ekonomickej literatúry, 1972, 240 s. info
  • KAUMAN, A. and R CRUON. Dynamické programovanie. Bratislavaa, 1969, 312 pp. Matematické metódy v ekonomike, Alfa. ISBN 302 - 063 - 69. info
  • NEMHAUSER, George, L. Introduction to Dynamic Programming. New York: John Wiley, 1966, 350 pp. ISBN 0-8247-8245-3. info
  • BELLMAN, Richard. Dynamic programming. Dover ed. Mineola, N.Y.: Dover Publications, 2003, xxv, 340. ISBN 0486428095. info
  • GEL'FAND, Izrail Moisejevič and Sergej Vasil'jevič FOMIN. Calculus of variations. Edited by Richard A. Silverman. Mineola, N. Y.: Dover Publications, 2000, vii, 232 s. ISBN 0-486-41448-5. info
  • ŠKRÁŠEK, Josef and Zdeněk TICHÝ. Základy aplikované matematiky. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1990, 853 s. ISBN 80-03-00111-0. info
Teaching methods
Lectures and exercises.
Assessment methods
The exam has both written and oral components. In the written part students solve particular examples. In the oral part a question concerning one of the topic I-IV (see the syllabus above) is given and the knowledge of basic concepts is required.

The conditions (especially regarding the form of the tests and exam) will be specified according to the epidemiological situation and valid restrictions.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Teacher's information
The lessons are usually in Czech or in English as needed, and the relevant terminology is always given with English equivalents. The target skills of the study include the ability to use the English language passively and actively in their own expertise and also in potential areas of application of mathematics. Assessment in all cases may be in Czech and English, at the student's choice.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M0160 Optimization

Faculty of Science
Spring 2020
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
doc. Mgr. Petr Zemánek, Ph.D. (lecturer)
Guaranteed by
doc. Mgr. Petr Zemánek, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Tue 14:00–15:50 M4,01024
  • Timetable of Seminar Groups:
M0160/01: Tue 16:00–17:50 M4,01024, P. Zemánek
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
After this course the studnets get knowledge and skill concerning basic methods of solutions of some optimization problems.
Learning outcomes
At the end of this course the students will be able to solve problems of the linear, integer, quadratic, and dynamic programming as well as basic problems of calculus of variations.
Syllabus
  • I. Linear programming.
  • Ia. Integer programming.
  • II. Quadratic programming.
  • III. Dynamic programming: Bellman optimization principle, finite deterministic and stochastic decision models, infinite steps models.
  • IV. Elements of the calculus of variations and discrete optimization: historical motivation, Euler-Lagrange equation and the first variation, second variation, elementary difference equations and recurrence relations, discrete calculus of variations.
Literature
    recommended literature
  • DOŠLÝ, Ondřej. Základy konvexní analýzy a optimalizace v R^n (Elements of convex analysis and optimization in R^n). 1st ed. Brno: Masarykova univerzita, 2005, 194 pp. ISBN 80-210-3905-1. info
  • DANTZIG, George Bernard and Mukund Narain THAPA. Linear programming. New York: Springer, 2003, xxv, 448 s. ISBN 0-387-98613-8. info
  • BAZARAA, Mokhtar S., John J. JARVIS and Hanif D. SHERALI. Linear programming and network flows. 2nd ed. New York: John Wiley & Sons, Inc., 1990, xiv+684 pp. ISBN 0-471-63681-9. info
  • KÜNZI, Hans P., Wilhelm KRELLE and Werner OETTLI. Nichtlineare Programmierung. Berlin: Springer-Verlag, 1962, 221 s. info
  • HAMALA, Milan. Nelineárne programovanie. 2. dopl. vyd. Bratislava: Alfa, vydavateľstvo technickej a ekonomickej literatúry, 1972, 240 s. info
  • KAUMAN, A. and R CRUON. Dynamické programovanie. Bratislavaa, 1969, 312 pp. Matematické metódy v ekonomike, Alfa. ISBN 302 - 063 - 69. info
  • NEMHAUSER, George, L. Introduction to Dynamic Programming. New York: John Wiley, 1966, 350 pp. ISBN 0-8247-8245-3. info
  • BELLMAN, Richard. Dynamic programming. Dover ed. Mineola, N.Y.: Dover Publications, 2003, xxv, 340. ISBN 0486428095. info
  • GEL'FAND, Izrail Moisejevič and Sergej Vasil'jevič FOMIN. Calculus of variations. Edited by Richard A. Silverman. Mineola, N. Y.: Dover Publications, 2000, vii, 232 s. ISBN 0-486-41448-5. info
    not specified
  • ŠKRÁŠEK, Josef and Zdeněk TICHÝ. Základy aplikované matematiky. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1990, 853 s. ISBN 80-03-00111-0. info
Teaching methods
Lectures and exercises.
Assessment methods
The exam has both written and oral components. In the written part students solve particular examples. In the oral part a question concerning one of the topic I-IV (see the syllabus above) is given and the knowledge of basic concepts is required.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Teacher's information
The lessons are usually in Czech or in English as needed, and the relevant terminology is always given with English equivalents. The target skills of the study include the ability to use the English language passively and actively in their own expertise and also in potential areas of application of mathematics. Assessment in all cases may be in Czech and English, at the student's choice.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M0160 Optimization Theory

Faculty of Science
Spring 2019
Extent and Intensity
2/2. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
doc. Mgr. Petr Zemánek, Ph.D. (lecturer)
Guaranteed by
prof. RNDr. Roman Šimon Hilscher, DSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 18. 2. to Fri 17. 5. Thu 10:00–11:50 M3,01023
  • Timetable of Seminar Groups:
M0160/01: Mon 18. 2. to Fri 17. 5. Thu 12:00–13:50 M3,01023, P. Zemánek
Prerequisites
The course of M5170 Mathematical Programming is suitable for the part devoted to the linear and quadratic programming.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course is a free continuation of the course M5170 Mathematical Programming. Students will get knowledge and skill concerning basic methods of solutions of some optimization problems.
Learning outcomes
At the end of this course the students will be able to solve problems of the linear, integer, quadratic, and dynamic programming as well as basic problems of calculus of variations.
Syllabus
  • I. Linear programming.
  • Ia. Integer programming.
  • II. Quadratic programming.
  • III. Dynamic programming: Bellman optimization principle, finite deterministic and stochastic decision models, infinite steps models.
  • IV. Elements of the calculus of variations and discrete optimization: historical motivation, Euler-Lagrange equation and the first variation, second variation, elementary difference equations and recurrence relations, discrete calculus of variations.
Literature
    recommended literature
  • DOŠLÝ, Ondřej. Základy konvexní analýzy a optimalizace v R^n (Elements of convex analysis and optimization in R^n). 1st ed. Brno: Masarykova univerzita, 2005, 194 pp. ISBN 80-210-3905-1. info
  • DANTZIG, George Bernard and Mukund Narain THAPA. Linear programming. New York: Springer, 2003, xxv, 448 s. ISBN 0-387-98613-8. info
  • BAZARAA, Mokhtar S., John J. JARVIS and Hanif D. SHERALI. Linear programming and network flows. 2nd ed. New York: John Wiley & Sons, Inc., 1990, xiv+684 pp. ISBN 0-471-63681-9. info
  • KÜNZI, Hans P., Wilhelm KRELLE and Werner OETTLI. Nichtlineare Programmierung. Berlin: Springer-Verlag, 1962, 221 s. info
  • HAMALA, Milan. Nelineárne programovanie. 2. dopl. vyd. Bratislava: Alfa, vydavateľstvo technickej a ekonomickej literatúry, 1972, 240 s. info
  • KAUMAN, A. and R CRUON. Dynamické programovanie. Bratislavaa, 1969, 312 pp. Matematické metódy v ekonomike, Alfa. ISBN 302 - 063 - 69. info
  • NEMHAUSER, George, L. Introduction to Dynamic Programming. New York: John Wiley, 1966, 350 pp. ISBN 0-8247-8245-3. info
  • BELLMAN, Richard. Dynamic programming. Dover ed. Mineola, N.Y.: Dover Publications, 2003, xxv, 340. ISBN 0486428095. info
  • GEL'FAND, Izrail Moisejevič and Sergej Vasil'jevič FOMIN. Calculus of variations. Edited by Richard A. Silverman. Mineola, N. Y.: Dover Publications, 2000, vii, 232 s. ISBN 0-486-41448-5. info
    not specified
  • ŠKRÁŠEK, Josef and Zdeněk TICHÝ. Základy aplikované matematiky. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1990, 853 s. ISBN 80-03-00111-0. info
Teaching methods
Theoretical lecture (2 hours) and seminar (2 hours).
Assessment methods
The exam has both written and oral components. In the written part students solve particular examples. In the oral part a question concerning one of the topic I-IV (see the syllabus above) is given and the knowledge of basic concepts is required.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M0160 Optimization Theory

Faculty of Science
spring 2018
Extent and Intensity
2/2. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
doc. Mgr. Petr Zemánek, Ph.D. (lecturer)
Guaranteed by
prof. RNDr. Roman Šimon Hilscher, DSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Fri 8:00–9:50 M3,01023
  • Timetable of Seminar Groups:
M0160/01: Fri 10:00–11:50 M3,01023, P. Zemánek
Prerequisites
The course of M5170 Mathematical Programming is suitable for the part devoted to the linear and quadratic programming.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course is a free continuation of the course M5170 Mathematical Programming. Students will get knowledge and skill concerning basic methods of solutions of some optimization problems.
Learning outcomes
At the end of this course the students will be able to solve problems of the linear, integer, quadratic, and dynamic programming as well as basic problems of calculus of variations.
Syllabus
  • I. Linear programming.
  • Ia. Integer programming.
  • II. Quadratic programming.
  • III. Dynamic programming: Bellman optimization principle, finite deterministic and stochastic decision models, infinite steps models.
  • IV. Elements of the calculus of variations and discrete optimization: historical motivation, Euler-Lagrange equation and the first variation, second variation, elementary difference equations and recurrence relations, discrete calculus of variations.
Literature
    recommended literature
  • DOŠLÝ, Ondřej. Základy konvexní analýzy a optimalizace v R^n (Elements of convex analysis and optimization in R^n). 1st ed. Brno: Masarykova univerzita, 2005, 194 pp. ISBN 80-210-3905-1. info
  • DANTZIG, George Bernard and Mukund Narain THAPA. Linear programming. New York: Springer, 2003, xxv, 448 s. ISBN 0-387-98613-8. info
  • BAZARAA, Mokhtar S., John J. JARVIS and Hanif D. SHERALI. Linear programming and network flows. 2nd ed. New York: John Wiley & Sons, Inc., 1990, xiv+684 pp. ISBN 0-471-63681-9. info
  • KÜNZI, Hans P., Wilhelm KRELLE and Werner OETTLI. Nichtlineare Programmierung. Berlin: Springer-Verlag, 1962, 221 s. info
  • HAMALA, Milan. Nelineárne programovanie. 2. dopl. vyd. Bratislava: Alfa, vydavateľstvo technickej a ekonomickej literatúry, 1972, 240 s. info
  • KAUMAN, A. and R CRUON. Dynamické programovanie. Bratislavaa, 1969, 312 pp. Matematické metódy v ekonomike, Alfa. ISBN 302 - 063 - 69. info
  • NEMHAUSER, George, L. Introduction to Dynamic Programming. New York: John Wiley, 1966, 350 pp. ISBN 0-8247-8245-3. info
  • BELLMAN, Richard. Dynamic programming. Dover ed. Mineola, N.Y.: Dover Publications, 2003, xxv, 340. ISBN 0486428095. info
  • GEL'FAND, Izrail Moisejevič and Sergej Vasil'jevič FOMIN. Calculus of variations. Edited by Richard A. Silverman. Mineola, N. Y.: Dover Publications, 2000, vii, 232 s. ISBN 0-486-41448-5. info
    not specified
  • ŠKRÁŠEK, Josef and Zdeněk TICHÝ. Základy aplikované matematiky. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1990, 853 s. ISBN 80-03-00111-0. info
Teaching methods
Theoretical lecture (2 hours) and seminar (2 hours).
Assessment methods
The exam has both written and oral components. In the written part students solve particular examples. In the oral part a question concerning one of the topic I-IV (see the syllabus above) is given and the knowledge of basic concepts is required.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M0160 Optimization Theory

Faculty of Science
Spring 2017
Extent and Intensity
2/1. 2 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
doc. Mgr. Petr Zemánek, Ph.D. (lecturer)
Guaranteed by
prof. RNDr. Roman Šimon Hilscher, DSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 20. 2. to Mon 22. 5. Thu 12:00–13:50 M4,01024
  • Timetable of Seminar Groups:
M0160/01: Mon 20. 2. to Mon 22. 5. Thu 14:00–14:50 M4,01024, P. Zemánek
Prerequisites
The course of M5170 Mathematical Programming is suitable for the part devoted to the linear and quadratic programming. Generally, knowledges from the courses of mathematical analysis.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course is a free continuation of the course M5170 Mathematical Programming and presents some optimization problems in more details. At the of this course the students will be able to solve problems of the linear, integer, quadratic, and dynamic programming as well as basic problems of calculus of variations.
Syllabus
  • I. Linear programming.
  • Ia. Integer programming.
  • II. Quadratic programming.
  • III. Dynamic programming: Bellman optimization principle, finite deterministic and stochastic decision models, infinite steps models.
  • IV. Elements of the calculus of variations and discrete optimization: historical motivation, Euler-Lagrange equation and the first variation, second variation, elementary difference equations and recurrence relations, discrete calculus of variations.
Literature
    recommended literature
  • DOŠLÝ, Ondřej. Základy konvexní analýzy a optimalizace v R^n (Elements of convex analysis and optimization in R^n). 1st ed. Brno: Masarykova univerzita, 2005, 194 pp. ISBN 80-210-3905-1. info
  • DANTZIG, George Bernard and Mukund Narain THAPA. Linear programming. New York: Springer, 2003, xxv, 448 s. ISBN 0-387-98613-8. info
  • BAZARAA, Mokhtar S., John J. JARVIS and Hanif D. SHERALI. Linear programming and network flows. 2nd ed. New York: John Wiley & Sons, Inc., 1990, xiv+684 pp. ISBN 0-471-63681-9. info
  • KÜNZI, Hans P., Wilhelm KRELLE and Werner OETTLI. Nichtlineare Programmierung. Berlin: Springer-Verlag, 1962, 221 s. info
  • HAMALA, Milan. Nelineárne programovanie. 2. dopl. vyd. Bratislava: Alfa, vydavateľstvo technickej a ekonomickej literatúry, 1972, 240 s. info
  • KAUMAN, A. and R CRUON. Dynamické programovanie. Bratislavaa, 1969, 312 pp. Matematické metódy v ekonomike, Alfa. ISBN 302 - 063 - 69. info
  • NEMHAUSER, George, L. Introduction to Dynamic Programming. New York: John Wiley, 1966, 350 pp. ISBN 0-8247-8245-3. info
  • BELLMAN, Richard. Dynamic programming. Dover ed. Mineola, N.Y.: Dover Publications, 2003, xxv, 340. ISBN 0486428095. info
  • GEL'FAND, Izrail Moisejevič and Sergej Vasil'jevič FOMIN. Calculus of variations. Edited by Richard A. Silverman. Mineola, N. Y.: Dover Publications, 2000, vii, 232 s. ISBN 0-486-41448-5. info
    not specified
  • ŠKRÁŠEK, Josef and Zdeněk TICHÝ. Základy aplikované matematiky. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1990, 853 s. ISBN 80-03-00111-0. info
Teaching methods
Theoretical lecture (2 hours) and seminar (1 hour).
Assessment methods
The exam has both written and oral components. In the written part students solve particular examples. In the oral part a question concerning one of the topic I-IV (see the syllabus above) is given and the knowledge of basic concepts is required.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M0160 Optimization Theory

Faculty of Science
Spring 2016
Extent and Intensity
2/1. 2 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
doc. Mgr. Petr Zemánek, Ph.D. (lecturer)
Guaranteed by
prof. RNDr. Ondřej Došlý, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Tue 14:00–15:50 M4,01024
  • Timetable of Seminar Groups:
M0160/01: Tue 16:00–16:50 M4,01024, P. Zemánek
Prerequisites
The course of M5170 Mathematical Programming is suitable for the part devoted to the linear and quadratic programming. Generally, knowledges from the courses of mathematical analysis.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course is a free continuation of the course M5170 Mathematical Programming and presents some optimization problems in more details. At the of this course the students will be able to solve problems of the linear, quadratic, and dynamic programming as well as basic problems of calculus of variations.
Syllabus
  • I. Linear programming.
  • II. Quadratic programming.
  • III. Dynamic programming: Bellman optimization principle, finite deterministic and stochastic decision models, infinite steps models.
  • IV. Elements of the calculus of variations and discrete optimization: historical motivation, Euler-Lagrange equation and the first variation, second variation, elementary difference equations and recurrence relations, discrete calculus of variations.
Literature
    recommended literature
  • DOŠLÝ, Ondřej. Základy konvexní analýzy a optimalizace v R^n (Elements of convex analysis and optimization in R^n). 1st ed. Brno: Masarykova univerzita, 2005, 194 pp. ISBN 80-210-3905-1. info
  • DANTZIG, George Bernard and Mukund Narain THAPA. Linear programming. New York: Springer, 2003, xxv, 448 s. ISBN 0-387-98613-8. info
  • BAZARAA, Mokhtar S., John J. JARVIS and Hanif D. SHERALI. Linear programming and network flows. 2nd ed. New York: John Wiley & Sons, Inc., 1990, xiv+684 pp. ISBN 0-471-63681-9. info
  • KÜNZI, Hans P., Wilhelm KRELLE and Werner OETTLI. Nichtlineare Programmierung. Berlin: Springer-Verlag, 1962, 221 s. info
  • HAMALA, Milan. Nelineárne programovanie. 2. dopl. vyd. Bratislava: Alfa, vydavateľstvo technickej a ekonomickej literatúry, 1972, 240 s. info
  • KAUMAN, A. and R CRUON. Dynamické programovanie. Bratislavaa, 1969, 312 pp. Matematické metódy v ekonomike, Alfa. ISBN 302 - 063 - 69. info
  • NEMHAUSER, George, L. Introduction to Dynamic Programming. New York: John Wiley, 1966, 350 pp. ISBN 0-8247-8245-3. info
  • BELLMAN, Richard. Dynamic programming. Dover ed. Mineola, N.Y.: Dover Publications, 2003, xxv, 340. ISBN 0486428095. info
  • GEL'FAND, Izrail Moisejevič and Sergej Vasil'jevič FOMIN. Calculus of variations. Edited by Richard A. Silverman. Mineola, N. Y.: Dover Publications, 2000, vii, 232 s. ISBN 0-486-41448-5. info
    not specified
  • ŠKRÁŠEK, Josef and Zdeněk TICHÝ. Základy aplikované matematiky. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1990, 853 s. ISBN 80-03-00111-0. info
Teaching methods
Theoretical lecture (2 hours) and seminar (1 hour).
Assessment methods
The exam has both written and oral components. In the written part students solve particular examples. In the oral part a question concerning one of the topic I-IV (see the syllabus above) is given and the knowledge of basic concepts is required.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M0160 Optimization Theory

Faculty of Science
Spring 2015
Extent and Intensity
2/1. 2 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
doc. Mgr. Petr Zemánek, Ph.D. (lecturer)
Guaranteed by
prof. RNDr. Ondřej Došlý, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Fri 11:00–12:50 M2,01021
  • Timetable of Seminar Groups:
M0160/01: Fri 13:00–13:50 M2,01021, P. Zemánek
Prerequisites
The course of M5170 Mathematical Programming is suitable for the part devoted to the linear and quadratic programming. Generally, knowledges from the course of Mathematical Analysis I-III are suitable.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course is a free continuation of the course M5170 Mathematical Programming and presents optimization methods which are not treated in that course. At the of this course the students will be able to solve problems of the linear, quadratic, and dynamic programming as well as basic problems of calculus of variations.
Syllabus
  • I. Linear programming.
  • II. Quadratic programming.
  • III. Dynamic programming: Bellman optimization principle, finite deterministic and stochastic decision models, infinite steps models - functional equation of dynamic programming.
  • IV. Elements of the calculus of variations and discrete optimization: historical motivation, Euler-Lagrange equation and the first variation, second variation, elementary difference equations and recurrence relations, discrete calculus of variations.
Literature
  • DOŠLÝ, Ondřej. Základy konvexní analýzy a optimalizace v R^n (Elements of convex analysis and optimization in R^n). 1st ed. Brno: Masarykova univerzita, 2005, 194 pp. ISBN 80-210-3905-1. info
  • DANTZIG, George Bernard and Mukund Narain THAPA. Linear programming. New York: Springer, 2003, xxv, 448 s. ISBN 0-387-98613-8. info
  • BAZARAA, Mokhtar S., John J. JARVIS and Hanif D. SHERALI. Linear programming and network flows. 2nd ed. New York: John Wiley & Sons, Inc., 1990, xiv+684 pp. ISBN 0-471-63681-9. info
  • NEMHAUSER, George, L. Introduction to Dynamic Programming. New York: John Wiley, 1966, 350 pp. ISBN 0-8247-8245-3. info
  • KAUMAN, A. and R CRUON. Dynamické programovanie. Bratislavaa, 1969, 312 pp. Matematické metódy v ekonomike, Alfa. ISBN 302 - 063 - 69. info
  • ŠKRÁŠEK, Josef and Zdeněk TICHÝ. Základy aplikované matematiky. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1990, 853 s. ISBN 80-03-00111-0. info
Teaching methods
Theoretical lecture with illustrative examples.
Assessment methods
The exam has both written and oral components. In the written part students solve particular examples. In the oral part a question concerning one of the topic I-IV (see the syllabus above) is given and the knowledge of basic concepts is required.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M0160 Optimization Theory

Faculty of Science
Spring 2014
Extent and Intensity
2/1. 2 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Ondřej Došlý, DrSc. (lecturer)
doc. Mgr. Petr Zemánek, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Ondřej Došlý, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Tue 15:00–16:50 M2,01021
  • Timetable of Seminar Groups:
M0160/01: Tue 17:00–17:50 M2,01021, O. Došlý
Prerequisites
The course of Mathematical Programming is supposed for the part devoted to quadratic programming, generally knowledges from the course of Mathematical Analysis I-III are supposed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course is a free continuation of the course Mathematical Programming (M5170) and presents optimization methods which are not treated in that course.
Syllabus
  • I. Quadratic programming in economic decision, methods of quadratic programming (continuation of the course Mathematical Programming M5171). II. Dynamic programming: Bellman optimization principle, finite deterministic and stochastic decision models, infinite steps models - functional equation of dynamic programming. III. Elements of the calculus of variations and discrete optimization: historical motivation, Euler-Lagrange equation and the first variation, second variation, elementary difference equations and recurrence relations, discrete calculus of variations.
Literature
  • DOŠLÝ, Ondřej. Základy konvexní analýzy a optimalizace v R^n (Elements of convex analysis and optimization in R^n). 1st ed. Brno: Masarykova univerzita, 2005, 194 pp. ISBN 80-210-3905-1. info
  • ŠKRÁŠEK, Josef and Zdeněk TICHÝ. Základy aplikované matematiky. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1990, 853 s. ISBN 80-03-00111-0. info
  • KAUMAN, A. and R CRUON. Dynamické programovanie. Bratislavaa, 1969, 312 pp. Matematické metódy v ekonomike, Alfa. ISBN 302 - 063 - 69. info
  • NEMHAUSER, George, L. Introduction to Dynamic Programming. New York: John Wiley, 1966, 350 pp. ISBN 0-8247-8245-3. info
Teaching methods
Theoretical lecture
Assessment methods
The course is finished by an oral exam. The student usually gets two questions. The knowledge of basic concepts of both two questions is needed to pass. What does it mean ``knowledge of the basic cenceps'' depends of a particular quastion which is a student given.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M0160 Optimization Theory

Faculty of Science
Spring 2013
Extent and Intensity
2/1. 2 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Ondřej Došlý, DrSc. (lecturer)
Guaranteed by
prof. RNDr. Ondřej Došlý, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Fri 8:00–9:50 M4,01024
  • Timetable of Seminar Groups:
M0160/01: Fri 10:00–10:50 M4,01024, O. Došlý
Prerequisites
The course of Mathematical Programming is supposed for the part devoted to quadratic programming, generally knowledges from the course of Mathematical Analysis I-III are supposed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course is a free continuation of the course Mathematical Programming (M5170) and presents optimization methods which are not treated in that course.
Syllabus
  • I. Quadratic programming in economic decision, methods of quadratic programming (continuation of the course Mathematical Programming M5171). II. Dynamic programming: Bellman optimization principle, finite deterministic and stochastic decision models, infinite steps models - functional equation of dynamic programming. III. Elements of the calculus of variations and discrete optimization: historical motivation, Euler-Lagrange equation and the first variation, second variation, elementary difference equations and recurrence relations, discrete calculus of variations.
Literature
  • DOŠLÝ, Ondřej. Základy konvexní analýzy a optimalizace v R^n (Elements of convex analysis and optimization in R^n). 1st ed. Brno: Masarykova univerzita, 2005, 194 pp. ISBN 80-210-3905-1. info
  • ŠKRÁŠEK, Josef and Zdeněk TICHÝ. Základy aplikované matematiky. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1990, 853 s. ISBN 80-03-00111-0. info
  • KAUMAN, A. and R CRUON. Dynamické programovanie. Bratislavaa, 1969, 312 pp. Matematické metódy v ekonomike, Alfa. ISBN 302 - 063 - 69. info
  • NEMHAUSER, George, L. Introduction to Dynamic Programming. New York: John Wiley, 1966, 350 pp. ISBN 0-8247-8245-3. info
Teaching methods
Theoretical lecture
Assessment methods
The course is finished by an oral exam. The student usually gets two questions. The knowledge of basic concepts of both two questions is needed to pass. What does it mean ``knowledge of the basic cenceps'' depends of a particular quastion which is a student given.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M0160 Optimization Theory

Faculty of Science
Spring 2012
Extent and Intensity
2/1. 2 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Ondřej Došlý, DrSc. (lecturer)
Guaranteed by
prof. RNDr. Ondřej Došlý, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Tue 16:00–17:50 M5,01013
  • Timetable of Seminar Groups:
M0160/01: Thu 14:00–14:50 M3,01023, O. Došlý
Prerequisites
The course of Mathematical Programming is supposed for the part devoted to quadratic programming, generally knowledges from the course of Mathematical Analysis I-III are supposed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course is a free continuation of the course Mathematical Programming (M5170) and presents optimization methods which are not treated in that course.
Syllabus
  • I. Quadratic programming in economic decision, methods of quadratic programming (continuation of the course Mathematical Programming M5171). II. Dynamic programming: Bellman optimization principle, finite deterministic and stochastic decision models, infinite steps models - functional equation of dynamic programming. III. Elements of the calculus of variations and discrete optimization: historical motivation, Euler-Lagrange equation and the first variation, second variation, elementary difference equations and recurrence relations, discrete calculus of variations.
Literature
  • ŠKRÁŠEK, Josef and Zdeněk TICHÝ. Základy aplikované matematiky. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1990, 853 s. ISBN 80-03-00111-0. info
  • KAUMAN, A. and R CRUON. Dynamické programovanie. Bratislavaa, 1969, 312 pp. Matematické metódy v ekonomike, Alfa. ISBN 302 - 063 - 69. info
  • NEMHAUSER, George, L. Introduction to Dynamic Programming. New York: John Wiley, 1966, 350 pp. ISBN 0-8247-8245-3. info
Teaching methods
Theoretical lecture
Assessment methods
The course is finished by an oral exam.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M0160 Optimization Theory

Faculty of Science
Spring 2011
Extent and Intensity
2/1. 2 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Ondřej Došlý, DrSc. (lecturer)
Guaranteed by
prof. RNDr. Ondřej Došlý, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Tue 14:00–15:50 M6,01011
  • Timetable of Seminar Groups:
M0160/01: Tue 16:00–16:50 M6,01011, O. Došlý
Prerequisites
The course of Mathematical Programming is supposed for the part devoted to quadratic programming, generally knowledges from the course of Mathematical Analysis I-III are supposed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course is a free continuation of the course Mathematical Programming (M5170) and presents optimization methods which are not treated in that course.
Syllabus
  • I. Quadratic programming in economic decision, methods of quadratic programming (continuation of the course Mathematical Programming M5171). II. Dynamic programming: Bellman optimization principle, finite deterministic and stochastic decision models, infinite steps models - functional equation of dynamic programming. III. Elements of the calculus of variations: historical motivation, Euler-Lagrange equation and the first variation, second variation. Elements of optimal control theory, Pontryagin principle.
Literature
  • DOŠLÝ, Ondřej. Základy konvexní analýzy a optimalizace v R^n (Elements of convex analysis and optimization in R^n). 1st ed. Brno: Masarykova univerzita, 2005, 194 pp. ISBN 80-210-3905-1. info
  • NEMHAUSER, George, L. Introduction to Dynamic Programming. New York: John Wiley, 1966, 350 pp. ISBN 0-8247-8245-3. info
  • KAUMAN, A. and R CRUON. Dynamické programovanie. Bratislavaa, 1969, 312 pp. Matematické metódy v ekonomike, Alfa. ISBN 302 - 063 - 69. info
  • ŠKRÁŠEK, Josef and Zdeněk TICHÝ. Základy aplikované matematiky. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1990, 853 s. ISBN 80-03-00111-0. info
  • LEWIS, Frank. Optimal Control. New York: John Wiley & Sons, 1986, 362 pp. A Wiley-Interscience Publication. ISBN 0-471-81240-4. info
Teaching methods
Theoretical lecture and excersise with illustrating examples
Assessment methods
The course is finished by an oral exam.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M0160 Optimalization

Faculty of Science
Spring 2010
Extent and Intensity
2/0. 2 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Zdeněk Pospíšil, Dr. (lecturer)
Guaranteed by
prof. RNDr. Ondřej Došlý, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Tue 18:00–19:50 M5,01013
Prerequisites
The course of Mathematical Programming is supposed for the part devoted to quadratic programming, generally knowledges from the course of Mathematical Analysis I-III are supposed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course is a free continuation of the course Mathematical Programming (M5170) and presents optimization methods which are not treated in that course.
Syllabus
  • I. Quadratic programming in economic decision, methods of quadratic programming (continuation of the course Mathematical Programming M5171). II. Dynamic programming: Bellman optimization principle, finite deterministic and stochastic decision models, infinite steps models - functional equation of dynamic programming. III. Elements of the calculus of variations and discrete optimization: historical motivation, Euler-Lagrange equation and the first variation, second variation, elementary difference equations and recurrence relations, discrete calculus of variations.
Literature
  • ŠKRÁŠEK, Josef and Zdeněk TICHÝ. Základy aplikované matematiky. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1990, 853 s. ISBN 80-03-00111-0. info
  • KAUMAN, A. and R CRUON. Dynamické programovanie. Bratislavaa, 1969, 312 pp. Matematické metódy v ekonomike, Alfa. ISBN 302 - 063 - 69. info
  • NEMHAUSER, George, L. Introduction to Dynamic Programming. New York: John Wiley, 1966, 350 pp. ISBN 0-8247-8245-3. info
Teaching methods
Theoretical lecture
Assessment methods
The course is finished by an oral exam.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M0160 Optimalization

Faculty of Science
Spring 2009
Extent and Intensity
2/0. 2 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Ondřej Došlý, DrSc. (lecturer)
Guaranteed by
prof. RNDr. Ondřej Došlý, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Thu 12:00–13:50 M2,01021
Prerequisites
The course of Mathematical Programming is supposed for the part devoted to quadratic programming, generally knowledges from the course of Mathematical Analysis I-III are supposed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course is a free continuation of the course Mathematical Programming (M5170) and presents optimization methods which are not treated in that course.
Syllabus
  • I. Quadratic programming in economic decision, methods of quadratic programming (continuation of the course Mathematical Programming M5171). II. Dynamic programming: Bellman optimization principle, finite deterministic and stochastic decision models, infinite steps models - functional equation of dynamic programming. III. Elements of the calculus of variations and discrete optimization: historical motivation, Euler-Lagrange equation and the first variation, second variation, elementary difference equations and recurrence relations, discrete calculus of variations.
Literature
  • ŠKRÁŠEK, Josef and Zdeněk TICHÝ. Základy aplikované matematiky. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1990, 853 s. ISBN 80-03-00111-0. info
  • KAUMAN, A. and R CRUON. Dynamické programovanie. Bratislavaa, 1969, 312 pp. Matematické metódy v ekonomike, Alfa. ISBN 302 - 063 - 69. info
  • NEMHAUSER, George, L. Introduction to Dynamic Programming. New York: John Wiley, 1966, 350 pp. ISBN 0-8247-8245-3. info
Assessment methods
The course is finished by an oral exam.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M0160 Optimalization

Faculty of Science
Spring 2008
Extent and Intensity
2/0. 2 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Ondřej Došlý, DrSc. (lecturer)
Guaranteed by
prof. RNDr. Ondřej Došlý, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Thu 10:00–11:50 UP1
Prerequisites
The course of Mathematical Programming is supposed for the part devoted to quadratic programming, generally knowledges from the course of Mathematical Analysis I-III are supposed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course is a free continuation of the course Mathematical Programming (M5170) and presents optimization methods which are not treated in that course.
Syllabus
  • I. Quadratic programming in economic decision, methods of quadratic programming (continuation of the course Mathematical Programming M5171). II. Dynamic programming: Bellman optimization principle, finite deterministic and stochastic decision models, infinite steps models - functional equation of dynamic programming. III. Elements of the calculus of variations and discrete optimization: historical motivation, Euler-Lagrange equation and the first variation, second variation, elementary difference equations and recurrence relations, discrete calculus of variations.
Literature
  • ŠKRÁŠEK, Josef and Zdeněk TICHÝ. Základy aplikované matematiky. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1990, 853 s. ISBN 80-03-00111-0. info
  • KAUMAN, A. and R CRUON. Dynamické programovanie. Bratislavaa, 1969, 312 pp. Matematické metódy v ekonomike, Alfa. ISBN 302 - 063 - 69. info
  • NEMHAUSER, George, L. Introduction to Dynamic Programming. New York: John Wiley, 1966, 350 pp. ISBN 0-8247-8245-3. info
Assessment methods (in Czech)
Přednáška zakončná kolokviem spočívajícím ve vypracováním kolokviální práce (5-10 str.).
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M0160 Optimalization

Faculty of Science
Spring 2007
Extent and Intensity
2/0. 2 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Ondřej Došlý, DrSc. (lecturer)
Guaranteed by
prof. RNDr. Ondřej Došlý, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. RNDr. Ondřej Došlý, DrSc.
Timetable
Mon 8:00–9:50 UP1
Prerequisites
The course of Mathematical Programming is supposed for the part devoted to quadratic programming, generally knowledges from the course of Mathematical Analysis I-III are supposed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course is a free continuation of the course Mathematical Programming (M5170) and presents optimization methods which are not treated in that course.
Syllabus
  • I. Quadratic programming in economic decision, methods of quadratic programming (continuation of the course Mathematical Programming M5171). II. Dynamic programming: Bellman optimization principle, finite deterministic and stochastic decision models, infinite steps models - functional equation of dynamic programming. III. Elements of the calculus of variations and discrete optimization: historical motivation, Euler-Lagrange equation and the first variation, second variation, elementary difference equations and recurrence relations, discrete calculus of variations.
Literature
  • ŠKRÁŠEK, Josef and Zdeněk TICHÝ. Základy aplikované matematiky. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1990, 853 s. ISBN 80-03-00111-0. info
  • KAUMAN, A. and R CRUON. Dynamické programovanie. Bratislavaa, 1969, 312 pp. Matematické metódy v ekonomike, Alfa. ISBN 302 - 063 - 69. info
  • NEMHAUSER, George, L. Introduction to Dynamic Programming. New York: John Wiley, 1966, 350 pp. ISBN 0-8247-8245-3. info
Assessment methods (in Czech)
Přednáška zakončná kolokviem spočívajícím ve vypracováním kolokviální práce (5-10 str.).
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M0160 Optimalization

Faculty of Science
Spring 2006
Extent and Intensity
2/0. 2 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Ondřej Došlý, DrSc. (lecturer)
Guaranteed by
prof. RNDr. Ondřej Došlý, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. RNDr. Ondřej Došlý, DrSc.
Timetable
Tue 15:00–16:50 UP2
Prerequisites
The course of Mathematical Programming is supposed for the part devoted to quadratic programming, generally knowledges from the course of Mathematical Analysis I-III are supposed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course is a free continuation of the course Mathematical Programming (M5170) and presents optimization methods which are not treated in that course.
Syllabus
  • I. Quadratic programming in economic decision, methods of quadratic programming (continuation of the course Mathematical Programming M5171). II. Dynamic programming: Bellman optimization principle, finite deterministic and stochastic decision models, infinite steps models - functional equation of dynamic programming. III. Elements of the calculus of variations and discrete optimization: historical motivation, Euler-Lagrange equation and the first variation, second variation, elementary difference equations and recurrence relations, discrete calculus of variations.
Literature
  • ŠKRÁŠEK, Josef and Zdeněk TICHÝ. Základy aplikované matematiky. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1990, 853 s. ISBN 80-03-00111-0. info
  • KAUMAN, A. and R CRUON. Dynamické programovanie. Bratislavaa, 1969, 312 pp. Matematické metódy v ekonomike, Alfa. ISBN 302 - 063 - 69. info
  • NEMHAUSER, George, L. Introduction to Dynamic Programming. New York: John Wiley, 1966, 350 pp. ISBN 0-8247-8245-3. info
Assessment methods (in Czech)
Přednáška zakončná kolokviem spočívajícím ve vypracováním kolokviální práce (5-10 str.).
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2003, Spring 2004, Spring 2005, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M0160 Optimalization

Faculty of Science
Spring 2005
Extent and Intensity
2/0. 2 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Ondřej Došlý, DrSc. (lecturer)
Guaranteed by
prof. RNDr. Ondřej Došlý, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. RNDr. Ondřej Došlý, DrSc.
Timetable
Thu 10:00–11:50 U1
Prerequisites
The course of Mathematical Programming is supposed for the part devoted to quadratic programming, generally knowledges from the course of Mathematical Analysis I-III are supposed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course is a free continuation of the course Mathematical Programming (M5170) and presents optimization methods which are not treated in that course.
Syllabus
  • I. Quadratic programming in economic decision, methods of quadratic programming (continuation of the course Mathematical Programming M5171). II. Dynamic programming: Bellman optimization principle, finite deterministic and stochastic decision models, infinite steps models - functional equation of dynamic programming. III. Elements of the calculus of variations and discrete optimization: historical motivation, Euler-Lagrange equation and the first variation, second variation, elementary difference equations and recurrence relations, discrete calculus of variations.
Literature
  • ŠKRÁŠEK, Josef and Zdeněk TICHÝ. Základy aplikované matematiky. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1990, 853 s. ISBN 80-03-00111-0. info
  • KAUMAN, A. and R CRUON. Dynamické programovanie. Bratislavaa, 1969, 312 pp. Matematické metódy v ekonomike, Alfa. ISBN 302 - 063 - 69. info
  • NEMHAUSER, George, L. Introduction to Dynamic Programming. New York: John Wiley, 1966, 350 pp. ISBN 0-8247-8245-3. info
Assessment methods (in Czech)
Přednáška zakončná kolokviem spočívajícím ve vypracováním kolokviální práce (5-10 str.).
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2003, Spring 2004, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M0160 Optimalization

Faculty of Science
Spring 2004
Extent and Intensity
2/0. 2 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Ondřej Došlý, DrSc. (lecturer)
Guaranteed by
prof. RNDr. Ondřej Došlý, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. RNDr. Ondřej Došlý, DrSc.
Prerequisites
The course of Mathematical Programming is supposed for the part devoted to quadratic programming, generally knowledges from the course of Mathematical Analysis I-III are supposed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course is a free continuation of the course Mathematical Programming (M5170) and presents optimization methods which are not treated in that course.
Syllabus
  • I. Quadratic programming in economic decision, methods of quadratic programming (continuation of the course Mathematical Programming M5171). II. Dynamic programming: Bellman optimization principle, finite deterministic and stochastic decision models, infinite steps models - functional equation of dynamic programming. III. Elements of the calculus of variations and discrete optimization: historical motivation, Euler-Lagrange equation and the first variation, second variation, elementary difference equations and recurrence relations, discrete calculus of variations.
Literature
  • ŠKRÁŠEK, Josef and Zdeněk TICHÝ. Základy aplikované matematiky. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1990, 853 s. ISBN 80-03-00111-0. info
  • KAUMAN, A. and R CRUON. Dynamické programovanie. Bratislavaa, 1969, 312 pp. Matematické metódy v ekonomike, Alfa. ISBN 302 - 063 - 69. info
  • NEMHAUSER, George, L. Introduction to Dynamic Programming. New York: John Wiley, 1966, 350 pp. ISBN 0-8247-8245-3. info
Assessment methods (in Czech)
Přednáška zakončná kolokviem spočívajícím ve vypracováním kolokviální práce (5-10 str.).
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2003, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M0160 Optimalizition

Faculty of Science
Spring 2003
Extent and Intensity
2/0. 2 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Ondřej Došlý, DrSc. (lecturer)
Guaranteed by
prof. RNDr. Ondřej Došlý, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. RNDr. Ondřej Došlý, DrSc.
Prerequisites
The course of Mathematical Programming is supposed for the part devoted to quadratic programming, generally knowledges from the course of Mathematical Analysis I-III are supposed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course is a free continuation of the course Mathematical Programming (M5170) and presents optimization methods which are not treated in that course.
Syllabus
  • I. Quadratic programming in economic decision, methods of quadratic programming (continuation of the course Mathematical Programming M5171). II. Dynamic programming: Bellman optimization principle, finite deterministic and stochastic decision models, infinite steps models - functional equation of dynamic programming. III. Elements of the calculus of variations and discrete optimization: historical motivation, Euler-Lagrange equation and the first variation, second variation, elementary difference equations and recurrence relations, discrete calculus of variations.
Literature
  • ŠKRÁŠEK, Josef and Zdeněk TICHÝ. Základy aplikované matematiky. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1990, 853 s. ISBN 80-03-00111-0. info
  • KAUMAN, A. and R CRUON. Dynamické programovanie. Bratislavaa, 1969, 312 pp. Matematické metódy v ekonomike, Alfa. ISBN 302 - 063 - 69. info
  • NEMHAUSER, George, L. Introduction to Dynamic Programming. New York: John Wiley, 1966, 350 pp. ISBN 0-8247-8245-3. info
Assessment methods (in Czech)
Přednáška zakončná kolokviem spočívajícím ve vypracováním kolokviální práce (5-10 str.).
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught once in two years.
The course is taught: every week.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M0160 Optimization Theory

Faculty of Science
spring 2012 - acreditation

The information about the term spring 2012 - acreditation is not made public

Extent and Intensity
2/1. 2 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Ondřej Došlý, DrSc. (lecturer)
Guaranteed by
prof. RNDr. Ondřej Došlý, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
The course of Mathematical Programming is supposed for the part devoted to quadratic programming, generally knowledges from the course of Mathematical Analysis I-III are supposed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course is a free continuation of the course Mathematical Programming (M5170) and presents optimization methods which are not treated in that course.
Syllabus
  • I. Quadratic programming in economic decision, methods of quadratic programming (continuation of the course Mathematical Programming M5171). II. Dynamic programming: Bellman optimization principle, finite deterministic and stochastic decision models, infinite steps models - functional equation of dynamic programming. III. Elements of the calculus of variations and discrete optimization: historical motivation, Euler-Lagrange equation and the first variation, second variation, elementary difference equations and recurrence relations, discrete calculus of variations.
Literature
  • ŠKRÁŠEK, Josef and Zdeněk TICHÝ. Základy aplikované matematiky. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1990, 853 s. ISBN 80-03-00111-0. info
  • KAUMAN, A. and R CRUON. Dynamické programovanie. Bratislavaa, 1969, 312 pp. Matematické metódy v ekonomike, Alfa. ISBN 302 - 063 - 69. info
  • NEMHAUSER, George, L. Introduction to Dynamic Programming. New York: John Wiley, 1966, 350 pp. ISBN 0-8247-8245-3. info
Teaching methods
Theoretical lecture
Assessment methods
The course is finished by an oral exam.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M0160 Theory of Optimalization

Faculty of Science
Spring 2011 - only for the accreditation
Extent and Intensity
2/1. 2 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Ondřej Došlý, DrSc. (lecturer)
Guaranteed by
prof. RNDr. Ondřej Došlý, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
The course of Mathematical Programming is supposed for the part devoted to quadratic programming, generally knowledges from the course of Mathematical Analysis I-III are supposed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course is a free continuation of the course Mathematical Programming (M5170) and presents optimization methods which are not treated in that course.
Syllabus
  • I. Quadratic programming in economic decision, methods of quadratic programming (continuation of the course Mathematical Programming M5171). II. Dynamic programming: Bellman optimization principle, finite deterministic and stochastic decision models, infinite steps models - functional equation of dynamic programming. III. Elements of the calculus of variations and discrete optimization: historical motivation, Euler-Lagrange equation and the first variation, second variation, elementary difference equations and recurrence relations, discrete calculus of variations.
Literature
  • ŠKRÁŠEK, Josef and Zdeněk TICHÝ. Základy aplikované matematiky. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1990, 853 s. ISBN 80-03-00111-0. info
  • KAUMAN, A. and R CRUON. Dynamické programovanie. Bratislavaa, 1969, 312 pp. Matematické metódy v ekonomike, Alfa. ISBN 302 - 063 - 69. info
  • NEMHAUSER, George, L. Introduction to Dynamic Programming. New York: John Wiley, 1966, 350 pp. ISBN 0-8247-8245-3. info
Teaching methods
Theoretical lecture
Assessment methods
The course is finished by an oral exam.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M0160 Optimalization

Faculty of Science
Spring 2008 - for the purpose of the accreditation
Extent and Intensity
2/0. 2 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Ondřej Došlý, DrSc. (lecturer)
Guaranteed by
prof. RNDr. Ondřej Došlý, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. RNDr. Ondřej Došlý, DrSc.
Prerequisites
The course of Mathematical Programming is supposed for the part devoted to quadratic programming, generally knowledges from the course of Mathematical Analysis I-III are supposed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course is a free continuation of the course Mathematical Programming (M5170) and presents optimization methods which are not treated in that course.
Syllabus
  • I. Quadratic programming in economic decision, methods of quadratic programming (continuation of the course Mathematical Programming M5171). II. Dynamic programming: Bellman optimization principle, finite deterministic and stochastic decision models, infinite steps models - functional equation of dynamic programming. III. Elements of the calculus of variations and discrete optimization: historical motivation, Euler-Lagrange equation and the first variation, second variation, elementary difference equations and recurrence relations, discrete calculus of variations.
Literature
  • ŠKRÁŠEK, Josef and Zdeněk TICHÝ. Základy aplikované matematiky. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1990, 853 s. ISBN 80-03-00111-0. info
  • KAUMAN, A. and R CRUON. Dynamické programovanie. Bratislavaa, 1969, 312 pp. Matematické metódy v ekonomike, Alfa. ISBN 302 - 063 - 69. info
  • NEMHAUSER, George, L. Introduction to Dynamic Programming. New York: John Wiley, 1966, 350 pp. ISBN 0-8247-8245-3. info
Assessment methods (in Czech)
Přednáška zakončná kolokviem spočívajícím ve vypracováním kolokviální práce (5-10 str.).
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Spring 2011 - only for the accreditation, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.
  • Enrolment Statistics (recent)