M5170 Mathematical Programming
Faculty of ScienceAutumn 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).
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 - Timetable
- Tue 14:00–15:50 M2,01021
- Timetable of Seminar Groups:
- 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
- Applied Mathematics for Multi-Branches Study (programme PřF, N-MA)
- Financial and Insurance Mathematics (programme PřF, B-MA)
- Mathematics (programme PřF, B-MA)
- Statistics and Data Analysis (programme PřF, B-MA)
- Statistics and Data Analysis (programme PřF, N-MA)
- Course objectives
- Students will get basic knowledge concerning mathematical programming, numerical methods of unconstrained optimization, and also convex analysis.
- Learning outcomes
- After passing the course, the student will be able:
(1) to define and interpret the basic notions used in the basic parts of convex analysis and to explain their mutual context;
(2) to formulate relevant mathematical theorems and statements and to explain methods of their proofs;
(3) to use effective techniques utilized in basic fields of convex analysis;
(4) to apply acquired pieces of knowledge for the solution of specific problems of convex programming and to some numerical methods of optimization including problems of applicative character. - Syllabus
- I. Convex analysis: Convex sets (basic concepts, convex hull, separation and supporting hyperplanes); Convex Functions (basic concepts, criteria of convexity for differentiable functions); Subgradient and Subdifferential; Fenchel transformation; Systems of linear and convex inequalities.
- II. Numerical methods of unconstrained minimization: One-dimensional minimization (brute-force search, dichotomous search, Fibonacci and golden ratio methods); Unconstrained optimization (Method of steepest descent, Newton method, Conjugate gradient method).
- III. Mathematical programming: Lagrange principle (necessary and sufficient conditions for optimality, Kuhn-Tucker conditions, basic concepts of convex programming); Duality in mathematical programming (dual problem, Kuhn-Tucker vector, weak duality, strong duality, saddle point); Dependence on parameters (Envelope Theorem, shadow price)
- Literature
- required literature
- Petr Zemánek, Optimalizace aneb Když méně je více (učební text), viz https://optimalizace.page.link/ucebni_text
- recommended literature
- DOŠLÝ, Ondřej. Základy konvexní analýzy a optimalizace v Rn. 1. vyd. Brno: Masarykova univerzita, 2005, viii, 185. ISBN 8021039051. info
- HAMALA, Milan. Nelineárne programovanie. 2., dopl. vyd. Bratislava: Alfa, vydavateľstvo technickej a ekonomickej literatúry, 1976, 240 s. info
- BERTSEKAS, Dimitri P. Convex Optimization Theory. Athena Scientific, 2009, 256 pp. ISBN 978-1-886529-31-1. info
- Convex analysis. Edited by R. Tyrrell Rockafellar. Princeton: Princeton University Press, 1970, xviii, 451. ISBN 0691080690. info
- BORWEIN, Jonathan M. and Adrian S. LEWIS. Convex analysis and nonlinear optimization : theory and examples. New York: Springer-Verlag, 2000, x, 273. ISBN 0387989404. info
- SUN, Wenyu and Ya-Xiang YUAN. Optimization Theory and Methods - Nonlinear Programming. New York: Springer, 2006, 687 pp. Springer Optimization and Its Applications, Vol. 1. ISBN 978-0-387-24975-9. info
- SUCHAREV, Aleksej Grigor‘jevič, Aleksandr Vasil'jevič TIMOCHOV and Vjačeslav Vasil'jevič FEDOROV. Kurs metodov optimizacii. Moskva: Nauka, 1986, 325 s. info
- Teaching methods
- Lectures and exercises.
- Assessment methods
- In order to be admitted to the exam, a semester project is required - the details are available in the study materials in IS. The standard lecture and seminar, the exam has both written and oral parts.
The conditions (especially regarding the form of the exam) will be specified according to the epidemiological situation and valid restrictions. - Language of instruction
- Czech
- Follow-Up Courses
- Further comments (probably available only in Czech)
- Study Materials
The course is taught annually.
M5170 Mathematical Programming
Faculty of ScienceAutumn 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
- Tue 12:00–13:50 M4,01024
- Timetable of Seminar Groups:
- 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
- Applied Mathematics for Multi-Branches Study (programme PřF, N-MA)
- Financial and Insurance Mathematics (programme PřF, B-MA)
- Mathematics (programme PřF, B-MA)
- Statistics and Data Analysis (programme PřF, B-MA)
- Statistics and Data Analysis (programme PřF, N-MA)
- Course objectives
- Students will get basic knowledge concerning mathematical programming, numerical methods of unconstrained optimization, and also convex analysis.
- Learning outcomes
- After passing the course, the student will be able:
(1) to define and interpret the basic notions used in the basic parts of convex analysis and to explain their mutual context;
(2) to formulate relevant mathematical theorems and statements and to explain methods of their proofs;
(3) to use effective techniques utilized in basic fields of convex analysis;
(4) to apply acquired pieces of knowledge for the solution of specific problems of convex programming and to some numerical methods of optimization including problems of applicative character. - Syllabus
- I. Convex analysis: Convex sets (basic concepts, convex hull, separation and supporting hyperplanes); Convex Functions (basic concepts, criteria of convexity for differentiable functions); Subgradient and Subdifferential; Fenchel transformation; Systems of linear and convex inequalities.
- II. Numerical methods of unconstrained minimization: One-dimensional minimization (brute-force search, dichotomous search, Fibonacci and golden ratio methods); Unconstrained optimization (Method of steepest descent, Newton method, Conjugate gradient method).
- III. Mathematical programming: Lagrange principle (necessary and sufficient conditions for optimality, Kuhn-Tucker conditions, basic concepts of convex programming); Duality in mathematical programming (dual problem, Kuhn-Tucker vector, weak duality, strong duality, saddle point); Dependence on parameters (Envelope Theorem, shadow price)
- Literature
- required literature
- Petr Zemánek, Optimalizace aneb Když méně je více (učební text), viz https://optimalizace.page.link/ucebni_text
- recommended literature
- DOŠLÝ, Ondřej. Základy konvexní analýzy a optimalizace v Rn. 1. vyd. Brno: Masarykova univerzita, 2005, viii, 185. ISBN 8021039051. info
- HAMALA, Milan. Nelineárne programovanie. 2., dopl. vyd. Bratislava: Alfa, vydavateľstvo technickej a ekonomickej literatúry, 1976, 240 s. info
- BERTSEKAS, Dimitri P. Convex Optimization Theory. Athena Scientific, 2009, 256 pp. ISBN 978-1-886529-31-1. info
- Convex analysis. Edited by R. Tyrrell Rockafellar. Princeton: Princeton University Press, 1970, xviii, 451. ISBN 0691080690. info
- BORWEIN, Jonathan M. and Adrian S. LEWIS. Convex analysis and nonlinear optimization : theory and examples. New York: Springer-Verlag, 2000, x, 273. ISBN 0387989404. info
- SUN, Wenyu and Ya-Xiang YUAN. Optimization Theory and Methods - Nonlinear Programming. New York: Springer, 2006, 687 pp. Springer Optimization and Its Applications, Vol. 1. ISBN 978-0-387-24975-9. info
- SUCHAREV, Aleksej Grigor‘jevič, Aleksandr Vasil'jevič TIMOCHOV and Vjačeslav Vasil'jevič FEDOROV. Kurs metodov optimizacii. Moskva: Nauka, 1986, 325 s. info
- Teaching methods
- Lectures and exercises.
- Assessment methods
- In order to be admitted to the exam, a semester project is required - the details are available in the study materials in IS. The standard lecture and seminar, the exam has both written and oral parts.
The conditions (especially regarding the form of the exam) will be specified according to the epidemiological situation and valid restrictions. - Language of instruction
- Czech
- Follow-Up Courses
- Further comments (probably available only in Czech)
- Study Materials
The course is taught annually.
M5170 Mathematical Programming
Faculty of ScienceAutumn 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)
- prof. RNDr. Roman Šimon Hilscher, DSc. (lecturer)
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 10:00–11:50 M2,01021
- Timetable of Seminar Groups:
- 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
- Applied Mathematics for Multi-Branches Study (programme PřF, N-MA)
- Financial and Insurance Mathematics (programme PřF, B-MA)
- Mathematics (programme PřF, B-MA)
- Statistics and Data Analysis (programme PřF, B-MA)
- Statistics and Data Analysis (programme PřF, N-MA)
- Course objectives
- Students will get basic knowledge concerning mathematical programming, numerical methods of unconstrained optimization, and also convex analysis.
- Learning outcomes
- After passing the course, the student will be able:
(1) to define and interpret the basic notions used in the basic parts of convex analysis and to explain their mutual context;
(2) to formulate relevant mathematical theorems and statements and to explain methods of their proofs;
(3) to use effective techniques utilized in basic fields of convex analysis;
(4) to apply acquired pieces of knowledge for the solution of specific problems of convex programming and to some numerical methods of optimization including problems of applicative character. - Syllabus
- I. Convex analysis: Convex sets (basic concepts, convex hull, separation and supporting hyperplanes); Convex Functions (basic concepts, criteria of convexity for differentiable functions); Subgradient and Subdifferential; Fenchel transformation; Systems of linear and convex inequalities.
- II. Numerical methods of unconstrained minimization: One-dimensional minimization (brute-force search, dichotomous search, Fibonacci and golden ratio methods); Unconstrained optimization (Method of steepest descent, Newton method, Conjugate gradient method).
- III. Mathematical programming: Lagrange principle (necessary and sufficient conditions for optimality, Kuhn-Tucker conditions, basic concepts of convex programming); Duality in mathematical programming (dual problem, Kuhn-Tucker vector, weak duality, strong duality, saddle point); Dependence on parameters (Envelope Theorem, shadow price)
- Literature
- required literature
- Petr Zemánek, Optimalizace aneb Když méně je více (učební text), viz https://optimalizace.page.link/ucebni_text
- recommended literature
- DOŠLÝ, Ondřej. Základy konvexní analýzy a optimalizace v Rn. 1. vyd. Brno: Masarykova univerzita, 2005, viii, 185. ISBN 8021039051. info
- HAMALA, Milan. Nelineárne programovanie. 2., dopl. vyd. Bratislava: Alfa, vydavateľstvo technickej a ekonomickej literatúry, 1976, 240 s. info
- BERTSEKAS, Dimitri P. Convex Optimization Theory. Athena Scientific, 2009, 256 pp. ISBN 978-1-886529-31-1. info
- Convex analysis. Edited by R. Tyrrell Rockafellar. Princeton: Princeton University Press, 1970, xviii, 451. ISBN 0691080690. info
- BORWEIN, Jonathan M. and Adrian S. LEWIS. Convex analysis and nonlinear optimization : theory and examples. New York: Springer-Verlag, 2000, x, 273. ISBN 0387989404. info
- SUN, Wenyu and Ya-Xiang YUAN. Optimization Theory and Methods - Nonlinear Programming. New York: Springer, 2006, 687 pp. Springer Optimization and Its Applications, Vol. 1. ISBN 978-0-387-24975-9. info
- SUCHAREV, Aleksej Grigor‘jevič, Aleksandr Vasil'jevič TIMOCHOV and Vjačeslav Vasil'jevič FEDOROV. Kurs metodov optimizacii. Moskva: Nauka, 1986, 325 s. info
- Teaching methods
- Lectures and exercises.
- Assessment methods
- In order to be admitted to the exam, a semester project is required - the details are available in the study materials in IS. The standard lecture and seminar, the exam has both written and oral parts.
The conditions (especially regarding the form of the exam) will be specified according to the epidemiological situation and valid restrictions. - Language of instruction
- Czech
- Follow-Up Courses
- Further comments (probably available only in Czech)
- Study Materials
The course is taught annually.
M5170 Mathematical Programming
Faculty of Scienceautumn 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
- 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 10:00–11:50 MP2,01014a
- Timetable of Seminar Groups:
- 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
- Applied Mathematics for Multi-Branches Study (programme PřF, N-MA)
- Financial and Insurance Mathematics (programme PřF, B-MA)
- Mathematics (programme PřF, B-MA)
- Statistics and Data Analysis (programme PřF, B-MA)
- Statistics and Data Analysis (programme PřF, N-MA)
- Course objectives
- Students will get basic knowledge concerning mathematical programming, numerical methods of unconstrained optimization, and also convex analysis.
- Learning outcomes
- After passing the course, the student will be able:
(1) to define and interpret the basic notions used in the basic parts of convex analysis and to explain their mutual context;
(2) to formulate relevant mathematical theorems and statements and to explain methods of their proofs;
(3) to use effective techniques utilized in basic fields of convex analysis;
(4) to apply acquired pieces of knowledge for the solution of specific problems of convex programming and to some numerical methods of optimization including problems of applicative character. - Syllabus
- I. Convex analysis: Convex sets (basic concepts, convex hull, separation and supporting hyperplanes); Convex Functions (basic concepts, criteria of convexity for differentiable functions); Subgradient and Subdifferential; Fenchel transformation; Systems of linear and convex inequalities.
- II. Numerical methods of unconstrained minimization: One-dimensional minimization (brute-force search, dichotomous search, Fibonacci and golden ratio methods); Unconstrained optimization (Method of steepest descent, Newton method, Conjugate gradient method).
- III. Mathematical programming: Lagrange principle (necessary and sufficient conditions for optimality, Kuhn-Tucker conditions, basic concepts of convex programming); Duality in mathematical programming (dual problem, Kuhn-Tucker vector, weak duality, strong duality, saddle point); Dependence on parameters (Envelope Theorem, shadow price)
- Literature
- recommended literature
- DOŠLÝ, Ondřej. Základy konvexní analýzy a optimalizace v Rn. 1. vyd. Brno: Masarykova univerzita, 2005, viii, 185. ISBN 8021039051. info
- HAMALA, Milan. Nelineárne programovanie. 2., dopl. vyd. Bratislava: Alfa, vydavateľstvo technickej a ekonomickej literatúry, 1976, 240 s. info
- BERTSEKAS, Dimitri P. Convex Optimization Theory. Athena Scientific, 2009, 256 pp. ISBN 978-1-886529-31-1. info
- Convex analysis. Edited by R. Tyrrell Rockafellar. Princeton: Princeton University Press, 1970, xviii, 451. ISBN 0691080690. info
- BORWEIN, Jonathan M. and Adrian S. LEWIS. Convex analysis and nonlinear optimization : theory and examples. New York: Springer-Verlag, 2000, x, 273. ISBN 0387989404. info
- SUN, Wenyu and Ya-Xiang YUAN. Optimization Theory and Methods - Nonlinear Programming. New York: Springer, 2006, 687 pp. Springer Optimization and Its Applications, Vol. 1. ISBN 978-0-387-24975-9. info
- SUCHAREV, Aleksej Grigor‘jevič, Aleksandr Vasil'jevič TIMOCHOV and Vjačeslav Vasil'jevič FEDOROV. Kurs metodov optimizacii. Moskva: Nauka, 1986, 325 s. info
- Teaching methods
- Lectures and exercises.
- Assessment methods
- In order to be admitted to the exam, a semester project is required - the details are available in the study materials in IS. The standard lecture and seminar, the exam has both written and oral parts.
The conditions (especially regarding the form of the exam) will be specified according to the epidemiological situation and valid restrictions. - Language of instruction
- Czech
- Follow-Up Courses
- Further comments (probably available only in Czech)
- Study Materials
The course is taught annually.
M5170 Mathematical Programming
Faculty of ScienceAutumn 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
- 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
- Tue 8:00–9:50 M1,01017
- Timetable of Seminar Groups:
- 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
- Applied Mathematics for Multi-Branches Study (programme PřF, N-MA)
- Financial and Insurance Mathematics (programme PřF, B-MA)
- Mathematics (programme PřF, B-MA)
- Statistics and Data Analysis (programme PřF, B-MA)
- Statistics and Data Analysis (programme PřF, N-MA)
- Course objectives
- Students will get basic knowledge concerning mathematical programming, numerical methods of unconstrained optimization, and also convex analysis.
- Learning outcomes
- After passing the course, the student will be able:
(1) to define and interpret the basic notions used in the basic parts of convex analysis and to explain their mutual context;
(2) to formulate relevant mathematical theorems and statements and to explain methods of their proofs;
(3) to use effective techniques utilized in basic fields of convex analysis;
(4) to apply acquired pieces of knowledge for the solution of specific problems of convex programming and to some numerical methods of optimization including problems of applicative character. - Syllabus
- I. Convex analysis: Convex sets (basic concepts, convex hull, separation and supporting hyperplanes); Convex Functions (basic concepts, criteria of convexity for differentiable functions); Subgradient and Subdifferential; Fenchel transformation; Systems of linear and convex inequalities.
- II. Numerical methods of unconstrained minimization: One-dimensional minimization (brute-force search, dichotomous search, Fibonacci and golden ratio methods); Unconstrained optimization (Method of steepest descent, Newton method, Conjugate gradient method).
- III. Mathematical programming: Lagrange principle (necessary and sufficient conditions for optimality, Kuhn-Tucker conditions, basic concepts of convex programming); Duality in mathematical programming (dual problem, Kuhn-Tucker vector, weak duality, strong duality, saddle point); Dependence on parameters (Envelope Theorem, shadow price)
- Literature
- recommended literature
- DOŠLÝ, Ondřej. Základy konvexní analýzy a optimalizace v Rn. 1. vyd. Brno: Masarykova univerzita, 2005, viii, 185. ISBN 8021039051. info
- HAMALA, Milan. Nelineárne programovanie. 2., dopl. vyd. Bratislava: Alfa, vydavateľstvo technickej a ekonomickej literatúry, 1976, 240 s. info
- BERTSEKAS, Dimitri P. Convex Optimization Theory. Athena Scientific, 2009, 256 pp. ISBN 978-1-886529-31-1. info
- Convex analysis. Edited by R. Tyrrell Rockafellar. Princeton: Princeton University Press, 1970, xviii, 451. ISBN 0691080690. info
- BORWEIN, Jonathan M. and Adrian S. LEWIS. Convex analysis and nonlinear optimization : theory and examples. New York: Springer-Verlag, 2000, x, 273. ISBN 0387989404. info
- SUN, Wenyu and Ya-Xiang YUAN. Optimization Theory and Methods - Nonlinear Programming. New York: Springer, 2006, 687 pp. Springer Optimization and Its Applications, Vol. 1. ISBN 978-0-387-24975-9. info
- SUCHAREV, Aleksej Grigor‘jevič, Aleksandr Vasil'jevič TIMOCHOV and Vjačeslav Vasil'jevič FEDOROV. Kurs metodov optimizacii. Moskva: Nauka, 1986, 325 s. info
- Teaching methods
- Lectures and exercises.
- Assessment methods
- In order to be admitted to the exam, a semester project is required - the details are available in the study materials in IS. The standard lecture and seminar, the exam has both written and oral parts.
The conditions (especially regarding the form of the exam) will be specified according to the epidemiological situation and valid restrictions. - Language of instruction
- Czech
- Follow-Up Courses
- Further comments (probably available only in Czech)
- Study Materials
The course is taught annually.
M5170 Mathematical Programming
Faculty of ScienceAutumn 2019
- 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
- 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 10:00–11:50 M1,01017
- Timetable of Seminar Groups:
- 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
- Applied Mathematics for Multi-Branches Study (programme PřF, N-MA)
- Financial and Insurance Mathematics (programme PřF, B-MA)
- Mathematics (programme PřF, B-MA)
- Statistics and Data Analysis (programme PřF, B-MA)
- Statistics and Data Analysis (programme PřF, N-MA)
- Course objectives
- Students will get basic knowledge concerning mathematical programming, numerical methods of unconstrained optimization, and also convex analysis.
- Learning outcomes
- After passing the course, the student will be able:
(1) to define and interpret the basic notions used in the basic parts of convex analysis and to explain their mutual context;
(2) to formulate relevant mathematical theorems and statements and to explain methods of their proofs;
(3) to use effective techniques utilized in basic fields of convex analysis;
(4) to apply acquired pieces of knowledge for the solution of specific problems of convex programming and to some numerical methods of optimization including problems of applicative character. - Syllabus
- I. Convex analysis: Convex sets (basic concepts, convex hull, separation and supporting hyperplanes); Convex Functions (basic concepts, criteria of convexity for differentiable functions); Subgradient and Subdifferential; Fenchel transformation; Systems of linear and convex inequalities.
- II. Numerical methods of unconstrained minimization: One-dimensional minimization (brute-force search, dichotomous search, Fibonacci and golden ratio methods); Unconstrained optimization (Method of steepest descent, Newton method, Conjugate gradient method).
- III. Mathematical programming: Lagrange principle (necessary and sufficient conditions for optimality, Kuhn-Tucker conditions, basic concepts of convex programming); Duality in mathematical programming (dual problem, Kuhn-Tucker vector, weak duality, strong duality, saddle point); Dependence on parameters (Envelope Theorem, shadow price)
- Literature
- recommended literature
- DOŠLÝ, Ondřej. Základy konvexní analýzy a optimalizace v Rn. 1. vyd. Brno: Masarykova univerzita, 2005, viii, 185. ISBN 8021039051. info
- HAMALA, Milan. Nelineárne programovanie. 2., dopl. vyd. Bratislava: Alfa, vydavateľstvo technickej a ekonomickej literatúry, 1976, 240 s. info
- BERTSEKAS, Dimitri P. Convex Optimization Theory. Athena Scientific, 2009, 256 pp. ISBN 978-1-886529-31-1. info
- Convex analysis. Edited by R. Tyrrell Rockafellar. Princeton: Princeton University Press, 1970, xviii, 451. ISBN 0691080690. info
- BORWEIN, Jonathan M. and Adrian S. LEWIS. Convex analysis and nonlinear optimization : theory and examples. New York: Springer-Verlag, 2000, x, 273. ISBN 0387989404. info
- SUN, Wenyu and Ya-Xiang YUAN. Optimization Theory and Methods - Nonlinear Programming. New York: Springer, 2006, 687 pp. Springer Optimization and Its Applications, Vol. 1. ISBN 978-0-387-24975-9. info
- SUCHAREV, Aleksej Grigor‘jevič, Aleksandr Vasil'jevič TIMOCHOV and Vjačeslav Vasil'jevič FEDOROV. Kurs metodov optimizacii. Moskva: Nauka, 1986, 325 s. info
- Teaching methods
- Lectures and exercises.
- Assessment methods
- In order to be admitted to the exam, a semester project is required - the details are available in the study materials in IS. The standard lecture and seminar, the exam has both written and oral parts.
- Language of instruction
- Czech
- Follow-Up Courses
- Further comments (probably available only in Czech)
- Study Materials
The course is taught annually.
M5170 Mathematical Programming
Faculty of ScienceAutumn 2018
- Extent and Intensity
- 2/1/0. 3 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 17. 9. to Fri 14. 12. Mon 14:00–15:50 M2,01021
- Timetable of Seminar Groups:
M5170/02: Mon 17. 9. to Fri 14. 12. Tue 15:00–15:50 M3,01023, 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
- Applied Mathematics for Multi-Branches Study (programme PřF, N-MA)
- Financial and Insurance Mathematics (programme PřF, B-MA)
- Mathematics (programme PřF, B-MA)
- Statistics and Data Analysis (programme PřF, B-MA)
- Statistics and Data Analysis (programme PřF, N-MA)
- Course objectives
- After passing the course, the student will be able:
(1) to define and interpret the basic notions used in the basic parts of convex analysis and to explain their mutual context;
(2) to formulate relevant mathematical theorems and statements and to explain methods of their proofs;
(3) to use effective techniques utilized in basic fields of convex analysis;
(4) to apply acquired pieces of knowledge for the solution of specific problems of convex programming and to some numerical methods of optimization including problems of applicative character. - Syllabus
- I. Convex analysis: Convex sets (basic concepts, convex hull, separation and supporting hyperplanes); Convex Functions (basic concepts, criteria of convexity for differentiable functions); Subgradient and Subdifferential; Fenchel transformation; Systems of linear and convex inequalities.
- II. Numerical methods of unconstrained minimization: One-dimensional minimization (brute-force search, dichotomous search, Fibonacci and golden ratio methods); Unconstrained optimization (Method of steepest descent, Newton method, Conjugate gradient method).
- III. Mathematical programming: Lagrange principle (necessary and sufficient conditions for optimality, Kuhn-Tucker conditions, basic concepts of convex programming); Duality in mathematical programming (dual problem, Kuhn-Tucker vector, weak duality, strong duality, saddle point); Dependence on parameters (Envelope Theorem, shadow price)
- Literature
- recommended literature
- DOŠLÝ, Ondřej. Základy konvexní analýzy a optimalizace v Rn. 1. vyd. Brno: Masarykova univerzita, 2005, viii, 185. ISBN 8021039051. info
- HAMALA, Milan. Nelineárne programovanie. 2., dopl. vyd. Bratislava: Alfa, vydavateľstvo technickej a ekonomickej literatúry, 1976, 240 s. info
- BERTSEKAS, Dimitri P. Convex Optimization Theory. Athena Scientific, 2009, 256 pp. ISBN 978-1-886529-31-1. info
- Convex analysis. Edited by R. Tyrrell Rockafellar. Princeton: Princeton University Press, 1970, xviii, 451. ISBN 0691080690. info
- BORWEIN, Jonathan M. and Adrian S. LEWIS. Convex analysis and nonlinear optimization : theory and examples. New York: Springer-Verlag, 2000, x, 273. ISBN 0387989404. info
- SUN, Wenyu and Ya-Xiang YUAN. Optimization Theory and Methods - Nonlinear Programming. New York: Springer, 2006, 687 pp. Springer Optimization and Its Applications, Vol. 1. ISBN 978-0-387-24975-9. info
- SUCHAREV, Aleksej Grigor‘jevič, Aleksandr Vasil'jevič TIMOCHOV and Vjačeslav Vasil'jevič FEDOROV. Kurs metodov optimizacii. Moskva: Nauka, 1986, 325 s. info
- Teaching methods
- Theoretical lecture and seminar
- Assessment methods
- In order to be admitted to the exam, a semester project is required - the details are available in the study materials in IS. The standard lecture and seminar, the exam has both written and oral parts.
- Language of instruction
- Czech
- Follow-Up Courses
- Further comments (probably available only in Czech)
- Study Materials
The course is taught annually.
M5170 Mathematical Programming
Faculty of Scienceautumn 2017
- Extent and Intensity
- 2/1/0. 3 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. 9. to Fri 15. 12. Tue 18:00–19:50 M1,01017
- Timetable of Seminar Groups:
M5170/02: Mon 18. 9. to Fri 15. 12. Wed 17:00–17:50 M6,01011, 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
- Applied Mathematics for Multi-Branches Study (programme PřF, N-MA)
- Financial and Insurance Mathematics (programme PřF, B-MA)
- Mathematics (programme PřF, B-MA)
- Statistics and Data Analysis (programme PřF, B-MA)
- Statistics and Data Analysis (programme PřF, N-MA)
- Course objectives
- After passing the course, the student will be able:
(1) to define and interpret the basic notions used in the basic parts of convex analysis and to explain their mutual context;
(2) to formulate relevant mathematical theorems and statements and to explain methods of their proofs;
(3) to use effective techniques utilized in basic fields of convex analysis;
(4) to apply acquired pieces of knowledge for the solution of specific problems of convex programming and to some numerical methods of optimization including problems of applicative character. - Syllabus
- I. Convex analysis: Convex sets (basic concepts, convex hull, separation and supporting hyperplanes); Convex Functions (basic concepts, criteria of convexity for differentiable functions); Subgradient and Subdifferential; Fenchel transformation; Systems of linear and convex inequalities.
- II. Numerical methods of unconstrained minimization: One-dimensional minimization (brute-force search, dichotomous search, Fibonacci and golden ratio methods); Unconstrained optimization (Method of steepest descent, Newton method, Conjugate gradient method).
- III. Mathematical programming: Lagrange principle (necessary and sufficient conditions for optimality, Kuhn-Tucker conditions, basic concepts of convex programming); Duality in mathematical programming (dual problem, Kuhn-Tucker vector, weak duality, strong duality, saddle point); Dependence on parameters (Envelope Theorem, shadow price)
- Literature
- recommended literature
- DOŠLÝ, Ondřej. Základy konvexní analýzy a optimalizace v Rn. 1. vyd. Brno: Masarykova univerzita, 2005, viii, 185. ISBN 8021039051. info
- HAMALA, Milan. Nelineárne programovanie. 2., dopl. vyd. Bratislava: Alfa, vydavateľstvo technickej a ekonomickej literatúry, 1976, 240 s. info
- BERTSEKAS, Dimitri P. Convex Optimization Theory. Athena Scientific, 2009, 256 pp. ISBN 978-1-886529-31-1. info
- Convex analysis. Edited by R. Tyrrell Rockafellar. Princeton: Princeton University Press, 1970, xviii, 451. ISBN 0691080690. info
- BORWEIN, Jonathan M. and Adrian S. LEWIS. Convex analysis and nonlinear optimization : theory and examples. New York: Springer-Verlag, 2000, x, 273. ISBN 0387989404. info
- SUN, Wenyu and Ya-Xiang YUAN. Optimization Theory and Methods - Nonlinear Programming. New York: Springer, 2006, 687 pp. Springer Optimization and Its Applications, Vol. 1. ISBN 978-0-387-24975-9. info
- SUCHAREV, Aleksej Grigor‘jevič, Aleksandr Vasil'jevič TIMOCHOV and Vjačeslav Vasil'jevič FEDOROV. Kurs metodov optimizacii. Moskva: Nauka, 1986, 325 s. info
- Teaching methods
- Theoretical lecture and seminar
- Assessment methods
- In order to be admitted to the exam, a semester project is required - the details are available in the study materials in IS. The standard lecture and seminar, the exam has both written and oral parts.
- Language of instruction
- Czech
- Follow-Up Courses
- Further comments (probably available only in Czech)
- Study Materials
The course is taught annually.
M5170 Mathematical Programming
Faculty of ScienceAutumn 2016
- Extent and Intensity
- 2/1/0. 3 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 19. 9. to Sun 18. 12. Wed 8:00–9:50 M1,01017
- Timetable of Seminar Groups:
M5170/02: Mon 19. 9. to Sun 18. 12. Fri 12:00–12:50 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
- Applied Mathematics for Multi-Branches Study (programme PřF, N-MA)
- Financial and Insurance Mathematics (programme PřF, B-MA)
- Mathematics (programme PřF, B-MA)
- Statistics and Data Analysis (programme PřF, B-MA)
- Statistics and Data Analysis (programme PřF, N-MA)
- Course objectives
- After passing the course, the student will be able:
(1) to define and interpret the basic notions used in the basic parts of convex analysis and to explain their mutual context;
(2) to formulate relevant mathematical theorems and statements and to explain methods of their proofs;
(3) to use effective techniques utilized in basic fields of convex analysis;
(4) to apply acquired pieces of knowledge for the solution of specific problems of convex programming and to some numerical methods of optimization including problems of applicative character. - Syllabus
- I. Convex analysis: Convex sets (basic concepts, convex hull, separation and supporting hyperplanes); Convex Functions (basic concepts, criteria of convexity for differentiable functions); Subgradient and Subdifferential; Fenchel transformation; Systems of linear and convex inequalities.
- II. Numerical methods of unconstrained minimization: One-dimensional minimization (brute-force search, dichotomous search, Fibonacci and golden ratio methods); Unconstrained optimization (Method of steepest descent, Newton method, Conjugate gradient method).
- III. Mathematical programming: Lagrange principle (necessary and sufficient conditions for optimality, Kuhn-Tucker conditions, basic concepts of convex programming); Duality in mathematical programming (dual problem, Kuhn-Tucker vector, weak duality, strong duality, saddle point); Dependence on parameters (Envelope Theorem, shadow price)
- Literature
- recommended literature
- DOŠLÝ, Ondřej. Základy konvexní analýzy a optimalizace v Rn. 1. vyd. Brno: Masarykova univerzita, 2005, viii, 185. ISBN 8021039051. info
- HAMALA, Milan. Nelineárne programovanie. 2., dopl. vyd. Bratislava: Alfa, vydavateľstvo technickej a ekonomickej literatúry, 1976, 240 s. info
- BERTSEKAS, Dimitri P. Convex Optimization Theory. Athena Scientific, 2009, 256 pp. ISBN 978-1-886529-31-1. info
- Convex analysis. Edited by R. Tyrrell Rockafellar. Princeton: Princeton University Press, 1970, xviii, 451. ISBN 0691080690. info
- BORWEIN, Jonathan M. and Adrian S. LEWIS. Convex analysis and nonlinear optimization : theory and examples. New York: Springer-Verlag, 2000, x, 273. ISBN 0387989404. info
- SUN, Wenyu and Ya-Xiang YUAN. Optimization Theory and Methods - Nonlinear Programming. New York: Springer, 2006, 687 pp. Springer Optimization and Its Applications, Vol. 1. ISBN 978-0-387-24975-9. info
- SUCHAREV, Aleksej Grigor‘jevič, Aleksandr Vasil'jevič TIMOCHOV and Vjačeslav Vasil'jevič FEDOROV. Kurs metodov optimizacii. Moskva: Nauka, 1986, 325 s. info
- Teaching methods
- Theoretical lecture and seminar
- Assessment methods
- In order to be admitted to the exam, a semester project is required - the details are available in the study materials in IS. The standard lecture and seminar, the exam has both written and oral parts.
- Language of instruction
- Czech
- Follow-Up Courses
- Further comments (probably available only in Czech)
- Study Materials
The course is taught annually.
M5170 Mathematical Programming
Faculty of ScienceAutumn 2015
- Extent and Intensity
- 2/1/0. 3 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
- Mon 8:00–9:50 M1,01017
- Timetable of Seminar Groups:
M5170/02: Tue 14:00–14:50 M5,01013, 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
- Applied Mathematics for Multi-Branches Study (programme PřF, N-MA)
- Financial and Insurance Mathematics (programme PřF, B-MA)
- Mathematics (programme PřF, B-MA)
- Statistics and Data Analysis (programme PřF, B-MA)
- Statistics and Data Analysis (programme PřF, N-MA)
- Course objectives
- After passing the course, the student will be able:
to define and interpret the basic notions used in the basic parts of convex analysis and to explain their mutual context;
to formulate relevant mathematical theorems and statements and to explain methods of their proofs;
to use effective techniques utilized in basic fields of convex analysis;
to apply acquired pieces of knowledge for the solution of specific problems of convex programming and to some numerical methods of optimization including problems of applicative character. - Syllabus
- I. Convex analysis: Convex sets (basic concepts, convex hull, separation and supporting hyperplanes); Convex Functions (basic concepts, criteria of convexity for differentiable functions); Subgradient and Subdifferential; Fenchel transformation; Systems of linear and convex inequalities.
- II. Mathematical programming, necessary and sufficient conditions for optimality, duality: Lagrange principle (Kuhn-Tucker conditions, basic concepts of convex progamming); Duality in mathematical programming (dual problem, Kuhn-Tucker vector, saddle point); Duality in special optimization problems (linear and quadratic)
- III. Numerical methods of minimization: One-dimensional minimization (Fibonaci and golden ratio methods); Unconstrained optimization (steepest slope method, method of conjugate gradients, Newton method).
- Literature
- DOŠLÝ, Ondřej. Základy konvexní analýzy a optimalizace v Rn. 1. vyd. Brno: Masarykova univerzita, 2005, viii, 185. ISBN 8021039051. info
- HAMALA, Milan. Nelineárne programovanie. 2., dopl. vyd. Bratislava: Alfa, vydavateľstvo technickej a ekonomickej literatúry, 1976, 240 s. info
- BERTSEKAS, Dimitri P. Convex Optimization Theory. Athena Scientific, 2009, 256 pp. ISBN 978-1-886529-31-1. info
- Convex analysis. Edited by R. Tyrrell Rockafellar. Princeton: Princeton University Press, 1970, xviii, 451. ISBN 0691080690. info
- BORWEIN, Jonathan M. and Adrian S. LEWIS. Convex analysis and nonlinear optimization : theory and examples. New York: Springer-Verlag, 2000, x, 273. ISBN 0387989404. info
- SUCHAREV, Aleksej Grigor‘jevič, Aleksandr Vasil'jevič TIMOCHOV and Vjačeslav Vasil'jevič FEDOROV. Kurs metodov optimizacii. Moskva: Nauka, 1986, 325 s. info
- Teaching methods
- Theoretical lecture and seminar
- Assessment methods
- The standard lecture and seminar, the exam has both written and oral parts.
- Language of instruction
- Czech
- Follow-Up Courses
- Further comments (probably available only in Czech)
- Study Materials
The course is taught annually.
M5170 Mathematical Programming
Faculty of ScienceAutumn 2014
- Extent and Intensity
- 2/1/0. 3 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 10:00–11:50 M1,01017
- Timetable of Seminar Groups:
- 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
- Mathematical and Statistical Methods in Economics (programme ESF, N-KME)
- Mathematics (programme PřF, B-MA)
- Mathematics (programme PřF, N-MA)
- Course objectives
- After passing the course, the student will be able:
to define and interpret the basic notions used in the basic parts of convex analysis and to explain their mutual context;
to formulate relevant mathematical theorems and statements and to explain methods of their proofs;
to use effective techniques utilized in basic fields of convex analysis;
to apply acquired pieces of knowledge for the solution of specific problems of convex programming and to some numerical methods of optimization including problems of applicative character. - Syllabus
- I. Convex analysis. Convex sets: basic concepts, convex hull, separation and supporting hyperplanes. Convex Functions: basic concepts, convexity criteria for differentiable functions, subgradient and subdifferential, Fenchel transformation, system of linear and convex inequalities. II. Duality, necessary and sufficient conditions for optimality. Lagrange principle, Kuhn-Tucker conditions, casic concepts of convex progamming. Duality in mathematical programming, dual problem, Kuhn-Tucker vector, saddle point. Duality in special optimization problems {linear and quadratic}. III. Numerical methods of minimization. Onedimensional minimization {Fibonaci and golden ratio methods} Unconstrained optimization (steepest slope method, method of conjugate gradients, Newton method}. Quadratic programming {Wolfe method and modofications, Thiel van de Panne method}.
- Literature
- Teaching methods
- Theoretical lecture and seminar
- Assessment methods
- The standard lecture and accompany exercise, the exam has written and oral part.
- Language of instruction
- Czech
- Follow-Up Courses
- Further comments (probably available only in Czech)
- Study Materials
The course is taught annually.
M5170 Mathematical Programming
Faculty of ScienceAutumn 2013
- Extent and Intensity
- 2/1/0. 3 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
- Thu 8:00–9:50 M1,01017
- Timetable of Seminar Groups:
- 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
- Mathematical and Statistical Methods in Economics (programme ESF, N-KME)
- Mathematics (programme PřF, B-MA)
- Mathematics (programme PřF, N-MA)
- Course objectives
- After passing the course, the student will be able:
to define and interpret the basic notions used in the basic parts of convex analysis and to explain their mutual context;
to formulate relevant mathematical theorems and statements and to explain methods of their proofs;
to use effective techniques utilized in basic fields of convex analysis;
to apply acquired pieces of knowledge for the solution of specific problems of convex programming and to some numerical methods of optimization including problems of applicative character. - Syllabus
- I. Convex analysis. Convex sets: basic concepts, convex hull, separation and supporting hyperplanes. Convex Functions: basic concepts, convexity criteria for differentiable functions, subgradient and subdifferential, Fenchel transformation, system of linear and convex inequalities. II. Duality, necessary and sufficient conditions for optimality. Lagrange principle, Kuhn-Tucker conditions, casic concepts of convex progamming. Duality in mathematical programming, dual problem, Kuhn-Tucker vector, saddle point. Duality in special optimization problems {linear and quadratic}. III. Numerical methods of minimization. Onedimensional minimization {Fibonaci and golden ratio methods} Unconstrained optimization (steepest slope method, method of conjugate gradients, Newton method}. Quadratic programming {Wolfe method and modofications, Thiel van de Panne method}.
- Literature
- Teaching methods
- Theoretical lecture and seminar
- Assessment methods
- The standard lecture and accompany exercise, the exam has written and oral part.
- Language of instruction
- Czech
- Follow-Up Courses
- Further comments (probably available only in Czech)
- Study Materials
The course is taught annually.
M5170 Mathematical Programming
Faculty of ScienceAutumn 2012
- Extent and Intensity
- 2/1/0. 3 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
- Mon 8:00–9:50 M1,01017
- Timetable of Seminar Groups:
- 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
- Mathematical and Statistical Methods in Economics (programme ESF, N-KME)
- Mathematics (programme PřF, B-MA)
- Mathematics (programme PřF, N-MA)
- Course objectives
- The aim of the course is to provide the basic fact of the convex and its application to optimization problems in finitedimensonal spaces. A particular attention is devoted to the convex programming and to some numerical methods of optimization.
- Syllabus
- I. Convex analysis. Convex sets: basic concepts, convex hull, separation and supporting hyperplanes. Convex Functions: basic concepts, convexity criteria for differentiable functions, subgradient and subdifferential, Fenchel transformation, system of linear and convex inequalities. II. Duality, necessary and sufficient conditions for optimality. Lagrange principle, Kuhn-Tucker conditions, casic concepts of convex progamming. Duality in mathematical programming, dual problem, Kuhn-Tucker vrctor, saddle point. Duality in special optimization problems {linear and quadratic}. III. Numerical methods of minimization. Onedimensional minimization {Fibonaci and golden ratio methods} Unconstrained optimization (steepest slope method, method of conjugate gradients, Newton method}. Quadratic programming {Wolfe method and modofications, Thiel van de Panne method}.
- Literature
- Teaching methods
- Theoretical lecture and seminar
- Assessment methods
- The standard lecture and accompany exercise, the exam has written and oral part.
- Language of instruction
- Czech
- Follow-Up Courses
- Further comments (probably available only in Czech)
- Study Materials
The course is taught annually.
M5170 Mathematical Programming
Faculty of ScienceAutumn 2011
- Extent and Intensity
- 2/1/0. 3 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
- Fri 10:00–11:50 M1,01017
- Timetable of Seminar Groups:
- Prerequisites (in Czech)
- KREDITY_MIN(30)
- 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
- Mathematical and Statistical Methods in Economics (programme ESF, N-KME)
- Mathematics (programme PřF, B-MA)
- Mathematics (programme PřF, M-MA)
- Mathematics (programme PřF, N-MA)
- Course objectives
- The aim of the course is to provide the basic fact of the convex and its application to optimization problems in finitedimensonal spaces. A particular attention is devoted to the convex programming and to some numerical methods of optimization.
- Syllabus
- I. Convex analysis. Convex sets: basic concepts, convex hull, separation and supporting hyperplanes. Convex Functions: basic concepts, convexity criteria for differentiable functions, subgradient and subdifferential, Fenchel transformation, system of linear and convex inequalities. II. Duality, necessary and sufficient conditions for optimality. Lagrange principle, Kuhn-Tucker conditions, casic concepts of convex progamming. Duality in mathematical programming, dual problem, Kuhn-Tucker vrctor, saddle point. Duality in special optimization problems {linear and quadratic}. III. Numerical methods of minimization. Onedimensional minimization {Fibonaci and golden ratio methods} Unconstrained optimization (steepest slope method, method of conjugate gradients, Newton method}. Quadratic programming {Wolfe method and modofications, Thiel van de Panne method}.
- Literature
- Teaching methods
- Theoretical lecture and seminar
- Assessment methods
- The standard lecture and accompany exercise, the exam has written and oral part.
- Language of instruction
- Czech
- Follow-Up Courses
- Further comments (probably available only in Czech)
- Study Materials
The course is taught annually.
M5170 Mathematical Programming
Faculty of ScienceAutumn 2010
- Extent and Intensity
- 2/1/0. 3 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
- Fri 10:00–11:50 M1,01017
- Timetable of Seminar Groups:
- Prerequisites (in Czech)
- KREDITY_MIN(30)
- 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
- Mathematical and Statistical Methods in Economics (programme ESF, N-KME)
- Mathematics (programme PřF, B-MA)
- Mathematics (programme PřF, M-MA)
- Mathematics (programme PřF, N-MA)
- Course objectives
- The aim of the course is to provide the basic fact of the convex and its application to optimization problems in finitedimensonal spaces. A particular attention is devoted to the convex programming and to some numerical methods of optimization.
- Syllabus
- I. Convex analysis. Convex sets: basic concepts, convex hull, separation and supporting hyperplanes. Convex Functions: basic concepts, convexity criteria for differentiable functions, subgradient and subdifferential, Fenchel transformation, system of linear and convex inequalities. II. Duality, necessary and sufficient conditions for optimality. Lagrange principle, Kuhn-Tucker conditions, casic concepts of convex progamming. Duality in mathematical programming, dual problem, Kuhn-Tucker vrctor, saddle point. Duality in special optimization problems {linear and quadratic}. III. Numerical methods of minimization. Onedimensional minimization {Fibonaci and golden ratio methods} Unconstrained optimization (steepest slope method, method of conjugate gradients, Newton method}. Quadratic programming {Wolfe method and modofications, Thiel van de Panne method}.
- Literature
- Teaching methods
- Theoretical lecture and seminar
- Assessment methods
- The standard lecture and accompany exercise, the exam has written and oral part.
- Language of instruction
- Czech
- Follow-Up Courses
- Further comments (probably available only in Czech)
- Study Materials
The course is taught annually.
M5170 Mathematical Programming
Faculty of ScienceAutumn 2009
- Extent and Intensity
- 2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
- Teacher(s)
- prof. RNDr. Ondřej Došlý, DrSc. (lecturer)
prof. RNDr. Roman Šimon Hilscher, DSc. (alternate examiner) - Guaranteed by
- prof. RNDr. Ondřej Došlý, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science - Timetable
- Thu 12:00–13:50 M1,01017
- Timetable of Seminar Groups:
- 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
- Mathematics (programme PřF, B-MA)
- Mathematics (programme PřF, M-MA)
- Mathematics (programme PřF, N-MA)
- Course objectives
- The aim of the course is to provide the basic fact of the convex and its application to optimization problems in finitedimensonal spaces. A particular attention is devoted to the convex programming and to some numerical methods of optimization.
- Syllabus
- I. Convex analysis. Convex sets: basic concepts, convex hull, separation and supporting hyperplanes. Convex Functions: basic concepts, convexity criteria for differentiable functions, subgradient and subdifferential, Fenchel transformation, system of linear and convex inequalities. II. Duality, necessary and sufficient conditions for optimality. Lagrange principle, Kuhn-Tucker conditions, casic concepts of convex progamming. Duality in mathematical programming, dual problem, Kuhn-Tucker vrctor, saddle point. Duality in special optimization problems {linear and quadratic}. III. Numerical methods of minimization. Onedimensional minimization {Fibonaci and golden ratio methods} Unconstrained optimization (steepest slope method, method of conjugate gradients, Newton method}. Quadratic programming {Wolfe method and modofications, Thiel van de Panne method}.
- Literature
- Teaching methods
- Theoretical lecture and seminar
- Assessment methods
- The standard lecture and accompany exercise, the exam has written and oral part.
- Language of instruction
- Czech
- Follow-Up Courses
- Further comments (probably available only in Czech)
- Study Materials
The course is taught annually.
M5170 Mathematical Programming
Faculty of ScienceAutumn 2008
- Extent and Intensity
- 2/1/0. 3 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
- Tue 15:00–16:50 M1,01017
- Timetable of Seminar Groups:
- 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
- Mathematics (programme PřF, B-MA)
- Mathematics (programme PřF, M-MA)
- Mathematics (programme PřF, N-MA)
- Course objectives
- The aim of the course is to provide the basic fact of the convex and its application to optimization problems in finitedimensonal spaces. A particular attention is devoted to the convex programming and to numerical some methods of optimization.
- Syllabus
- I. Convex analysis. Convex sets: basic concepts, convex hull, separation and supporting hyperplanes. Convex Functions: basic concepts, convexity criteria for differentiable functions, subgradient and subdifferential, Fenchel transformation, system of linear and convex inequalities. II. Duality, necessary and sufficient conditions for optimality. Lagrange principle, Kuhn-Tucker conditions, casic concepts of convex progamming. Duality in mathematical programming, dual problem, Kuhn-Tucker vrctor, saddle point. Duality in special optimization problems {linear and quadratic}. III. Numerical methods of minimization. Onedimensional minimization {Fibonaci and golden ratio methods} Unconstrained optimization (steepest slope method, method of conjugate gradients, Newton method}. Quadratic programming {Wolfe method and modofications, Thiel van de Panne method}.
- Literature
- Assessment methods
- The standard lecture and accompany exercise, the exam has written and oral part.
- Language of instruction
- Czech
- Follow-Up Courses
- Further comments (probably available only in Czech)
- The course is taught annually.
M5170 Mathematical Programming
Faculty of ScienceAutumn 2007
- Extent and Intensity
- 2/1/0. 3 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
- Tue 16:00–17:50 N41
- Timetable of Seminar Groups:
- 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
- Mathematics (programme PřF, B-MA)
- Mathematics (programme PřF, M-MA)
- Mathematics (programme PřF, N-MA)
- Course objectives
- The aim of the course is to provide the basic fact of the convex and its application to optimization problems in finitedimensonal spaces. A particular attention is devoted to the convex programming and to numerical some methods of optimization.
- Syllabus
- I. Convex analysis. Convex sets: basic concepts, convex hull, separation and supporting hyperplanes. Convex Functions: basic concepts, convexity criteria for differentiable functions, subgradient and subdifferential, Fenchel transformation, system of linear and convex inequalities. II. Duality, necessary and sufficient conditions for optimality. Lagrange principle, Kuhn-Tucker conditions, casic concepts of convex progamming. Duality in mathematical programming, dual problem, Kuhn-Tucker vrctor, saddle point. Duality in special optimization problems {linear and quadratic}. III. Numerical methods of minimization. Onedimensional minimization {Fibonaci and golden ratio methods} Unconstrained optimization (steepest slope method, method of conjugate gradients, Newton method}. Quadratic programming {Wolfe method and modofications, Thiel van de Panne method}.
- Literature
- Assessment methods (in Czech)
- Standardní přednáška a cvičení, zkouška má písemnou i ústní část.
- Language of instruction
- Czech
- Follow-Up Courses
- Further comments (probably available only in Czech)
- The course is taught annually.
M5170 Mathematical Programming
Faculty of ScienceAutumn 2006
- Extent and Intensity
- 2/1/0. 3 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
- Fri 10:00–11:50 N41
- Timetable of Seminar Groups:
- Prerequisites (in Czech)
- M4110 Linear 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
- Mathematics (programme PřF, B-MA)
- Mathematics (programme PřF, M-MA)
- Mathematics (programme PřF, N-MA)
- Course objectives
- The aim of the course is to provide the basic fact of the convex and its application to optimization problems in finitedimensonal spaces. A particular attention is devoted to the convex programming and to numerical some methods of optimization.
- Syllabus
- I. Convex analysis. Convex sets: basic concepts, convex hull, separation and supporting hyperplanes. Convex Functions: basic concepts, convexity criteria for differentiable functions, subgradient and subdifferential, Fenchel transformation, system of linear and convex inequalities. II. Duality, necessary and sufficient conditions for optimality. Lagrange principle, Kuhn-Tucker conditions, casic concepts of convex progamming. Duality in mathematical programming, dual problem, Kuhn-Tucker vrctor, saddle point. Duality in special optimization problems {linear and quadratic}. III. Numerical methods of minimization. Onedimensional minimization {Fibonaci and golden ratio methods} Unconstrained optimization (steepest slope method, method of conjugate gradients, Newton method}. Quadratic programming {Wolfe method and modofications, Thiel van de Panne method}.
- Literature
- Assessment methods (in Czech)
- Standardní přednáška a cvičení, zkouška má písemnou i ústní část.
- Language of instruction
- Czech
- Follow-Up Courses
- Further comments (probably available only in Czech)
- The course can also be completed outside the examination period.
The course is taught annually.
M5170 Mathematical Programming
Faculty of ScienceAutumn 2005
- Extent and Intensity
- 2/1/0. 3 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
- Fri 10:00–11:50 N21
- Timetable of Seminar Groups:
- Prerequisites (in Czech)
- M4110 Linear 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
- Mathematics (programme PřF, B-MA)
- Mathematics (programme PřF, M-MA)
- Mathematics (programme PřF, N-MA)
- Course objectives
- The aim of the course is to provide the basic fact of the convex and its application to optimization problems in finitedimensonal spaces. A particular attention is devoted to the convex programming and to numerical some methods of optimization.
- Syllabus
- I. Convex analysis. Convex sets: basic concepts, convex hull, separation and supporting hyperplanes. Convex Functions: basic concepts, convexity criteria for differentiable functions, subgradient and subdifferential, Fenchel transformation, system of linear and convex inequalities. II. Duality, necessary and sufficient conditions for optimality. Lagrange principle, Kuhn-Tucker conditions, casic concepts of convex progamming. Duality in mathematical programming, dual problem, Kuhn-Tucker vrctor, saddle point. Duality in special optimization problems {linear and quadratic}. III. Numerical methods of minimization. Onedimensional minimization {Fibonaci and golden ratio methods} Unconstrained optimization (steepest slope method, method of conjugate gradients, Newton method}. Quadratic programming {Wolfe method and modofications, Thiel van de Panne method}.
- Literature
- Assessment methods (in Czech)
- Standardní přednáška a cvičení, zkouška má písemnou i ústní část.
- Language of instruction
- Czech
- Follow-Up Courses
- Further comments (probably available only in Czech)
- The course can also be completed outside the examination period.
The course is taught annually.
M5170 Mathematical Programming
Faculty of ScienceAutumn 2004
- Extent and Intensity
- 2/1/0. 3 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 12:00–13:50 UP1
- Timetable of Seminar Groups:
- Prerequisites (in Czech)
- M4110 Linear 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
- there are 6 fields of study the course is directly associated with, display
- Course objectives
- The aim of the course is to provide the basic fact of the convex and its application to optimization problems in finitedimensonal spaces. A particular attention is devoted to the convex programming and to numerical some methods of optimization.
- Syllabus
- I. Convex analysis. Convex sets: basic concepts, convex hull, separation and supporting hyperplanes. Convex Functions: basic concepts, convexity criteria for differentiable functions, subgradient and subdifferential, Fenchel transformation, system of linear and convex inequalities. II. Duality, necessary and sufficient conditions for optimality. Lagrange principle, Kuhn-Tucker conditions, casic concepts of convex progamming. Duality in mathematical programming, dual problem, Kuhn-Tucker vrctor, saddle point. Duality in special optimization problems {linear and quadratic}. III. Numerical methods of minimization. Onedimensional minimization {Fibonaci and golden ratio methods} Unconstrained optimization (steepest slope method, method of conjugate gradients, Newton method}. Quadratic programming {Wolfe method and modofications, Thiel van de Panne method}.
- Literature
- Assessment methods (in Czech)
- Standardní přednáška a cvičení, zkouška má písemnou i ústní část.
- Language of instruction
- Czech
- Follow-Up Courses
- Further comments (probably available only in Czech)
- The course can also be completed outside the examination period.
The course is taught annually.
M5170 Mathematical Programming
Faculty of ScienceAutumn 2003
- Extent and Intensity
- 2/1/0. 3 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 of Seminar Groups
- M5170/01: No timetable has been entered into IS. O. Došlý
- Prerequisites (in Czech)
- M4110 Linear 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
- Mathematics (programme PřF, B-MA)
- Mathematics (programme PřF, M-MA)
- Mathematics (programme PřF, N-MA)
- Course objectives
- The aim of the course is to provide the basic fact of the convex and its application to optimization problems in finitedimensonal spaces. A particular attention is devoted to the convex programming and to numerical some methods of optimization.
- Syllabus
- I. Convex analysis. Convex sets: basic concepts, convex hull, separation and supporting hyperplanes. Convex Functions: basic concepts, convexity criteria for differentiable functions, subgradient and subdifferential, Fenchel transformation, system of linear and convex inequalities. II. Duality, necessary and sufficient conditions for optimality. Lagrange principle, Kuhn-Tucker conditions, casic concepts of convex progamming. Duality in mathematical programming, dual problem, Kuhn-Tucker vrctor, saddle point. Duality in special optimization problems {linear and quadratic}. III. Numerical methods of minimization. Onedimensional minimization {Fibonaci and golden ratio methods} Unconstrained optimization (steepest slope method, method of conjugate gradients, Newton method}. Quadratic programming {Wolfe method and modofications, Thiel van de Panne method}.
- Literature
- Assessment methods (in Czech)
- Standardní přednáška a cvičení, zkouška má písemnou i ústní část.
- Language of instruction
- Czech
- Follow-Up Courses
- Further comments (probably available only in Czech)
- The course can also be completed outside the examination period.
The course is taught annually.
M5170 Mathematical Programming
Faculty of ScienceAutumn 2002
- Extent and Intensity
- 2/1/0. 3 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 (in Czech)
- M4110 Linear 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
- Mathematics (programme PřF, B-MA)
- Mathematics (programme PřF, M-MA)
- Mathematics (programme PřF, N-MA)
- Course objectives
- The aim of the course is to provide the basic fact of the convex and its application to optimization problems in finitedimensonal spaces. A particular attention is devoted to the convex programming and to numerical some methods of optimization.
- Syllabus
- I. Convex analysis. Convex sets: basic concepts, convex hull, separation and supporting hyperplanes. Convex Functions: basic concepts, convexity criteria for differentiable functions, subgradient and subdifferential, Fenchel transformation, system of linear and convex inequalities. II. Duality, necessary and sufficient conditions for optimality. Lagrange principle, Kuhn-Tucker conditions, casic concepts of convex progamming. Duality in mathematical programming, dual problem, Kuhn-Tucker vrctor, saddle point. Duality in special optimization problems {linear and quadratic}. III. Numerical methods of minimization. Onedimensional minimization {Fibonaci and golden ratio methods} Unconstrained optimization (steepest slope method, method of conjugate gradients, Newton method}. Quadratic programming {Wolfe method and modofications, Thiel van de Panne method}.
- Literature
- Assessment methods (in Czech)
- Standardní přednáška a cvičení, zkouška má písemnou i ústní část.
- Language of instruction
- Czech
- Follow-Up Courses
- Further comments (probably available only in Czech)
- The course can also be completed outside the examination period.
The course is taught annually.
The course is taught: every week.
M5170 Complex Analysis
Faculty of ScienceAutumn 2000
- Extent and Intensity
- 4/2/0. 9 credit(s). Type of Completion: zk (examination).
- Teacher(s)
- doc. RNDr. Josef Kalas, CSc. (lecturer)
- Guaranteed by
- doc. RNDr. Josef Kalas, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Josef Kalas, CSc. - Prerequisites (in Czech)
- M3100 Mathematical Analysis III
- 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
- Mathematics (programme PřF, M-MA)
- Mathematics (programme PřF, N-MA)
- Course objectives
- Topological concepts. Complex functions, complex differentiability, Cauchy-Riemann equations. Complex integration. Cauchy's theorem, Cauchy's integral formula. Fundamental properties of holomorphic functions. Power and Laurent series. Isolated singularities, calculus of residues and its applications. Entire functions. Meromorphic functions. Basic principles of conformal mapping theory.
- Literature
- ČERNÝ, Ilja. Analýza v komplexním oboru. 1. vyd. Praha: Academia, 1983, 822 s. info
- NOVÁK, Vítězslav. Analýza v komplexním oboru. 1. vyd. Praha: Státní pedagogické nakladatelství, 1984, 103 s. info
- Bicadze, A. V. Osnovy teorii analitičeskich funkcij komplexnogo peremennogo. nauka, Moskva, 1969.
- JEVGRAFOV, Marat Andrejevič. Funkce komplexní proměnné. Translated by Ladislav Průcha. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1981, 379 s. URL info
- JEVGRAFOV, Marat Andrejevič. Sbírka úloh z teorie funkcí komplexní proměnné. Translated by Anna Něničková - Věra Maňasová - Eva Nováková. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1976, 542 s. URL info
- Language of instruction
- Czech
- Further Comments
- The course can also be completed outside the examination period.
The course is taught annually.
The course is taught: every week.
M5170 Complex Analysis
Faculty of ScienceAutumn 1999
- Extent and Intensity
- 2/1/0. 9 credit(s). Type of Completion: zk (examination).
- Teacher(s)
- doc. RNDr. Josef Kalas, CSc. (lecturer)
- Guaranteed by
- doc. RNDr. Josef Kalas, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Josef Kalas, CSc. - Prerequisites (in Czech)
- M3100 Mathematical Analysis III && M2110 Linear Algebra II
- 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
- Mathematics (programme PřF, M-MA)
- Mathematics (programme PřF, N-MA)
- Syllabus
- Topological concepts. Complex functions, complex differentiability, Cauchy-Riemann equations. Complex integration. Cauchy's theorem, Cauchy's integral formula. Fundamental properties of holomorphic functions. Power and Laurent series. Isolated singularities, calculus of residues and its applications. Entire functions. Meromorphic functions. Basic principles of conformal mapping theory.
- Literature
- ČERNÝ, Ilja. Analýza v komplexním oboru. 1. vyd. Praha: Academia, 1983, 822 s. info
- NOVÁK, Vítězslav. Analýza v komplexním oboru. 1. vyd. Praha: Státní pedagogické nakladatelství, 1984, 103 s. info
- Bicadze, A. V. Osnovy teorii analitičeskich funkcij komplexnogo peremennogo. nauka, Moskva, 1969.
- JEVGRAFOV, Marat Andrejevič. Funkce komplexní proměnné. Translated by Ladislav Průcha. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1981, 379 s. URL info
- JEVGRAFOV, Marat Andrejevič. Sbírka úloh z teorie funkcí komplexní proměnné. Translated by Anna Něničková - Věra Maňasová - Eva Nováková. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1976, 542 s. URL info
- Language of instruction
- Czech
- Further Comments
- The course can also be completed outside the examination period.
The course is taught annually.
The course is taught: every week.
M5170 Mathematical Programming
Faculty of ScienceAutumn 2011 - acreditation
The information about the term Autumn 2011 - acreditation is not made public
- Extent and Intensity
- 2/1/0. 3 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 (in Czech)
- KREDITY_MIN(30)
- 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
- Mathematical and Statistical Methods in Economics (programme ESF, N-KME)
- Mathematics (programme PřF, B-MA)
- Mathematics (programme PřF, M-MA)
- Mathematics (programme PřF, N-MA)
- Course objectives
- The aim of the course is to provide the basic fact of the convex and its application to optimization problems in finitedimensonal spaces. A particular attention is devoted to the convex programming and to some numerical methods of optimization.
- Syllabus
- I. Convex analysis. Convex sets: basic concepts, convex hull, separation and supporting hyperplanes. Convex Functions: basic concepts, convexity criteria for differentiable functions, subgradient and subdifferential, Fenchel transformation, system of linear and convex inequalities. II. Duality, necessary and sufficient conditions for optimality. Lagrange principle, Kuhn-Tucker conditions, casic concepts of convex progamming. Duality in mathematical programming, dual problem, Kuhn-Tucker vrctor, saddle point. Duality in special optimization problems {linear and quadratic}. III. Numerical methods of minimization. Onedimensional minimization {Fibonaci and golden ratio methods} Unconstrained optimization (steepest slope method, method of conjugate gradients, Newton method}. Quadratic programming {Wolfe method and modofications, Thiel van de Panne method}.
- Literature
- Teaching methods
- Theoretical lecture and seminar
- Assessment methods
- The standard lecture and accompany exercise, the exam has written and oral part.
- Language of instruction
- Czech
- Follow-Up Courses
- Further comments (probably available only in Czech)
- The course is taught annually.
The course is taught: every week.
M5170 Mathematical Programming
Faculty of ScienceAutumn 2010 - only for the accreditation
- Extent and Intensity
- 2/1/0. 3 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 (in Czech)
- KREDITY_MIN(30)
- 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
- Mathematical and Statistical Methods in Economics (programme ESF, N-KME)
- Mathematics (programme PřF, B-MA)
- Mathematics (programme PřF, M-MA)
- Mathematics (programme PřF, N-MA)
- Course objectives
- The aim of the course is to provide the basic fact of the convex and its application to optimization problems in finitedimensonal spaces. A particular attention is devoted to the convex programming and to some numerical methods of optimization.
- Syllabus
- I. Convex analysis. Convex sets: basic concepts, convex hull, separation and supporting hyperplanes. Convex Functions: basic concepts, convexity criteria for differentiable functions, subgradient and subdifferential, Fenchel transformation, system of linear and convex inequalities. II. Duality, necessary and sufficient conditions for optimality. Lagrange principle, Kuhn-Tucker conditions, casic concepts of convex progamming. Duality in mathematical programming, dual problem, Kuhn-Tucker vrctor, saddle point. Duality in special optimization problems {linear and quadratic}. III. Numerical methods of minimization. Onedimensional minimization {Fibonaci and golden ratio methods} Unconstrained optimization (steepest slope method, method of conjugate gradients, Newton method}. Quadratic programming {Wolfe method and modofications, Thiel van de Panne method}.
- Literature
- Teaching methods
- Theoretical lecture and seminar
- Assessment methods
- The standard lecture and accompany exercise, the exam has written and oral part.
- Language of instruction
- Czech
- Follow-Up Courses
- Further comments (probably available only in Czech)
- The course is taught annually.
The course is taught: every week.
M5170 Mathematical Programming
Faculty of ScienceAutumn 2007 - for the purpose of the accreditation
- Extent and Intensity
- 2/1/0. 3 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 (in Czech)
- M4110 Linear 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
- Mathematics (programme PřF, B-MA)
- Mathematics (programme PřF, M-MA)
- Mathematics (programme PřF, N-MA)
- Course objectives
- The aim of the course is to provide the basic fact of the convex and its application to optimization problems in finitedimensonal spaces. A particular attention is devoted to the convex programming and to numerical some methods of optimization.
- Syllabus
- I. Convex analysis. Convex sets: basic concepts, convex hull, separation and supporting hyperplanes. Convex Functions: basic concepts, convexity criteria for differentiable functions, subgradient and subdifferential, Fenchel transformation, system of linear and convex inequalities. II. Duality, necessary and sufficient conditions for optimality. Lagrange principle, Kuhn-Tucker conditions, casic concepts of convex progamming. Duality in mathematical programming, dual problem, Kuhn-Tucker vrctor, saddle point. Duality in special optimization problems {linear and quadratic}. III. Numerical methods of minimization. Onedimensional minimization {Fibonaci and golden ratio methods} Unconstrained optimization (steepest slope method, method of conjugate gradients, Newton method}. Quadratic programming {Wolfe method and modofications, Thiel van de Panne method}.
- Literature
- Assessment methods (in Czech)
- Standardní přednáška a cvičení, zkouška má písemnou i ústní část.
- Language of instruction
- Czech
- Follow-Up Courses
- Further comments (probably available only in Czech)
- The course can also be completed outside the examination period.
The course is taught annually.
The course is taught: every week.
- Enrolment Statistics (recent)