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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
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

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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 -

To receive course credit, it is necessary to obtain a sufficient number of points on the credit test, which is part of the final exam. Points can also be earned for active participation in the exercise sessions. Attendance at the exercise sessions is not mandatory.

More detailed information about course credit requirements is available on the website:

https://kam.mff.cuni.cz/~hladik/DSO

Last update: Hladík Milan, prof. Mgr., Ph.D. (19.02.2026)

Literature -

Electronic textbook (for the continuous part):

https://kam.mff.cuni.cz/~hladik/DSO/text_dso_en.pdf

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 -

The exam requirements correspond to the course syllabus in the scope covered during lectures and exercise sessions. The exam consists of a written and an oral part. The exam may take place either in person or in a remote format.

Last update: Hladík Milan, prof. Mgr., Ph.D. (19.02.2026)

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)