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Course, academic year 2018/2019
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Fundamentals of Continuous Optimization - NMMB438
Title in English: Základy spojité optimalizace
Guaranteed by: Department of Algebra (32-KA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2018 to 2019
Semester: summer
E-Credits: 6
Hours per week, examination: summer s.:2/2 C+Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech, English
Teaching methods: full-time
Is provided by: NOPT046
Guarantor: doc. Mgr. Milan Hladík, Ph.D.
prof. RNDr. Martin Loebl, CSc.
Class: M Mgr. MMIB
M Mgr. MMIB > Povinně volitelné
Classification: Mathematics > Optimization
Incompatibility : NOPT046
Interchangeability : NOPT046
Annotation -
Last update: Mgr. Jan Kynčl, Ph.D. (25.01.2018)
Review course covering fundamental fields of optimization, incl. computational methods. There are countless examples from almost all branches of human doing leading to problems coming under this discipline. Introduction to several other courses specialized in the solution of particular classes of optimization problems. Previous knowledge of linear programming, e.g. from NOPT048 Linear Programming and Combinatorial Optimization (formerly Optimization Methods) is advisable (but not required).
Course completion requirements -
Last update: Andreas Emil Feldmann, Dr. (14.02.2018)

For the English version of the tutorial:

The tutorial will feature two quizzes, one midterm quiz on the topic of discrete optimization and one final quiz on the topic of continuous optimization. You need to obtain 60% of the total points of both quizzes to obtain the credit for the tutorial.

Literature -
Last update: doc. Mgr. Milan Hladík, Ph.D. (04.05.2015)

M.S. Bazaraa, H.D. Sherali, C.M. Shetty: Nonlinear Programming, Wiley, New Jersey, 2006.

S. Boyd, L. Vandenberghe: Convex Optimization, Cambridge University Press, 2009.

W.J. Cook, W.H. Cunningham, W.R. Pulleyblank, A. Schrijver. Combinatorial Optimization. Wiley, New York, 1998.

Requirements to the exam -
Last update: Andreas Emil Feldmann, Dr. (14.02.2018)

For the English version of the lecture:

To participate in the exam of the lecture you need to obtain the credit for the tutorial. The exam is semi-oral, and you have three tries.

Syllabus -
Last update: Andreas Emil Feldmann, Dr. (14.02.2018)

Fundamentals of discrete optimization:

  • Introduction, examples of optimization and examples of techniques. Analysis of algorithms, implementation and complexity.
  • Shortest paths and minimum spanning trees and relations.
  • Maximum matching and applications, relation to flows in networks. Algorithms for matchings. Postman problem.
  • Traveling salesman problem (TSP): heuristics, applications and relations.
  • Comparisons of hard and polynomial problems.

Fundamentals of continuous optimization:

  • Convex functions and sets
  • Convex optimization
  • Quadratic programming
  • Cone programming and duality
  • Karush-Kuhn-Tucker optimality conditions
  • Basic methods
  • Programming with uncertain data, robust optimization

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