IA102 Linear and Integer Optimization Tasks and their Solutions

Faculty of Informatics
Spring 2007
Extent and Intensity
2/2. 4 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: z (credit).
Teacher(s)
prof. RNDr. Petr Hliněný, Ph.D. (lecturer)
Guaranteed by
prof. RNDr. Mojmír Křetínský, CSc.
Department of Computer Science – Faculty of Informatics
Contact Person: prof. RNDr. Petr Hliněný, Ph.D.
Timetable
Thu 14:00–15:50 B410, Thu 16:00–17:50 B410
Prerequisites
Mathematical knowledge on course levels of basic linear algebra (vectors, matrices, linear equations) and discrete mathematics (relations, graphs). Introductory knowledge of topology is also welcome.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
The capacity limit for the course is 50 student(s).
Current registration and enrolment status: enrolled: 0/50, only registered: 0/50, only registered with preference (fields directly associated with the programme): 0/50
fields of study / plans the course is directly associated with
there are 7 fields of study the course is directly associated with, display
Course objectives
This subject presents students with basic types of optimization tasks (combinatorial, linear, and integer optimization), and teaches some basic solution methods. The main focus is on explaining and understanding the simplex method of linear optimization, and the branch-and-bound method of integer optimization. Other tasks briefly mentioned are network flows, scheduling, or TSP problems.
The lectures shall explain mathematical background used to solve those optimization problems, and the tutorials shall deal with examples of practically motivated tasks, and of optimization software usage.
Syllabus
  • The greedy algorithm and its applications.
  • Network flows with applications, duality to cuts.
  • Linear optimization (linear programming) problem.
  • Convexity and polyhedra in LP.
  • Duality of LP problems.
  • The simplex method for linear programming.
  • Implementing the simplex method.
  • Degenerated steps, looping, complexity.
  • Integer or discrete optimization problem (IP).
  • The branch-and-bound method in a shortcut.
  • Theory and implementation of branch-and-bound.
  • Combinatorial optimization problems.
  • The art of proper formulation of MIP.
  • Advanced discrete optimization topics.
Literature
  • P. Hliněný, Optimalizační úlohy, http://www.fi.muni.cz/~hlineny/Teaching/OU/OU-text07.pdf.
  • NEMHAUSER, George L. and Laurence A. WOLSEY. Integer and combinatorial oprimization. New York: John Wiley & Sons, 1988, 763 s. ISBN 0-471-82819-X. info
  • JANÁČEK, Jaroslav. Matematické Programování. Žilina, SK: EDIS Žilinská Univerzita, 2003. info
Assessment methods (in Czech)
Written individual homework assignment (one), and a subsequent oral exam.
Language of instruction
English
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Teacher's information
http://www.fi.muni.cz/~hlineny/Teaching/OU.html
The course is also listed under the following terms Autumn 2005, Spring 2009, Spring 2011.
  • Enrolment Statistics (Spring 2007, recent)
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