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Course, academic year 2023/2024
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Fundamentals of Continuous Optimization - NMMB438
Title: Základy spojité optimalizace
Guaranteed by: Department of Algebra (32-KA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2021
Semester: summer
E-Credits: 6
Hours per week, examination: summer s.:2/2, C+Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: Czech, English
Teaching methods: full-time
Teaching methods: full-time
Is provided by: NOPT046
Guarantor: prof. 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 -
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).
Last update: Kynčl Jan, doc. Mgr., Ph.D. (25.01.2018)
Course completion requirements -

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.

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

Electronic textbook (for the continuous part):

Further references:

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.

Last update: Hladík Milan, prof. Mgr., Ph.D. (30.09.2021)
Requirements to the exam -

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.

In exceptional situations, the exam can have a distance form.

Last update: Hladík Milan, prof. Mgr., Ph.D. (28.04.2020)
Syllabus -

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

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