IA102 Linear and Integer Optimization Tasks and their Solutions

Faculty of Informatics
Spring 2011
Extent and Intensity
2/1. 3 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
Wed 9:00–11:50 G123
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 18 fields of study the course is directly associated with, display
Course objectives
This subject presents students with basic types of optimization tasks (e.g., combinatorial, linear, and integer optimization), and teaches the most common solution methods. The main focus is on explaining and understanding (not memorizing!) the presented solution methods, including their thorough mathematical background, so that the students would be able to combine these methods with other approaches in solving nonstandard optimization problems. At the end of the course students should be able to: understand and explain the network-flow algorithm, the simplex method, and the branch-and-bound algorithm; formulate suitable and sound mathematical models of practical optimization problems; and use available tools to solve these problems.
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
Teaching methods
This is an advanced course, taught mostly in English (with also Czech materials), and conducted quite informally (a seminar-type lecturing). Students are expected to actively participate in all the lectures and tutorials.
Assessment methods
Evaluation is based on a mandatory written individual homework assignment (one essay), and on a subsequent oral exam.
Language of instruction
English
Further comments (probably available only in Czech)
Study Materials
The course is taught once in two years.
Teacher's information
http://is.muni.cz/el/1433/jaro2011/IA102/index.qwarp
The course is also listed under the following terms Autumn 2005, Spring 2007, Spring 2009.
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