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Course, academic year 2018/2019
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Optimization and variational analysis - NMEK603
Title in English: 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 [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech
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
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)


Requirements to the exam -
Last update: doc. RNDr. Petr Lachout, CSc. (11.10.2017)

The exam is oral.

Examination is checking knowledge of all matters read 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

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