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Optimization and variational analysis - NMEK603

Title:	Optimalizace a variační analýza
Guaranteed by:	Department of Probability and Mathematical Statistics (32-KPMS)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2016
Semester:	both
E-Credits:	3
Hours per week, examination:	2/0, Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time
Note:	you can enroll for the course repeatedly you can enroll for the course in winter and in summer semester

Guarantor:	doc. RNDr. Petr Lachout, CSc.
Class:	Pravděp. a statistika, ekonometrie a fin. mat.
Classification:	Mathematics > Optimization
Is interchangeable with:	NEKN027, NEKN028

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Annotation -

Last update: T_KPMS (06.05.2014)

The lecture is oriented to base of modern optimization and stability in stochastic programming. The lecture is devoted to doctoral students.

Aim of the course -

Last update: T_KPMS (06.05.2014)

Lecture builds up base of modern nonconvex optimization and development of stability in stochastic programming.

The theory is applied to particular stochastic optimization problems.

Course completion requirements -

Last update: doc. RNDr. Petr Lachout, CSc. (11.10.2017)

The course is finalized by exam.

Literature - Czech

Last update: T_KPMS (06.05.2014)

[1] Bonnans, J. F.; Shapiro, A.: Perturbation Analysis of Optimization Problems. Springer-Verlag, New York, 2000.

[2] Rockafellar, R.T.; Wets, R. J.-B.: Variational Analysis, Springer, Berlin 1998.

[3] Ruszczyński, A.; Shapiro, A; Eds.: "Stochastic Programming. Handbooks in OR & MS, volume 10,". Elsevier, Amsterdam, 2003.

[4] Shapiro, A.; Dentcheva, D.; Ruszczyński, A.: "Lectures on Stochastic Programming: Modeling and Theory". MPS-SIAM, Philadelphia, 2009.

Teaching methods -

Last update: T_KPMS (06.05.2014)

Lecture.

Requirements to the exam -

Last update: doc. RNDr. Petr Lachout, CSc. (14.02.2024)

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Requirements to exam

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The exam is oral.

Examination is checking knowledge of all topics read at the lecture and parts given to self-study by the course lecturer.

Syllabus -

Last update: T_KPMS (06.05.2014)

Variational Analysis

1) Convex analysis in finite dimension.

2) Cones and cosmic closure.

3) Set convergence.

4) Set-valued mappings.

5) Epi-convergence.

6) Variation analysis.

7) Subgradient and subdiferential.

8) Lipschitz properties.

9) Legendre-Fenchel duality.

Sensitivity of stochastic programming

1) Stability in stochastic programming.

2) Methods of parametric optimization. Probabilistic metrics.

3) Methods of asymptotic and robust statistics.

Entry requirements -

Last update: doc. RNDr. Petr Lachout, CSc. (30.05.2018)

basic of optimization theory, convex analysis