## Module Handbook

• Dynamischer Default-Fachbereich geändert auf MAT

# Module MAT-52-16-M-7

## Module Identification

Module Number Module Name CP (Effort)
MAT-52-16-M-7 Robust Optimization 9.0 CP (270 h)

## Basedata

CP, Effort 9.0 CP = 270 h 1 Sem. irreg. [7] Master (Advanced) [EN] English Ruzika, Stefan, Prof. Dr. (PROF | DEPT: MAT) Krumke, Sven Oliver, Prof. Dr. (PROF | DEPT: MAT) Ruzika, Stefan, Prof. Dr. (PROF | DEPT: MAT) Schöbel, Anita, Prof. Dr. (PROF | DEPT: MAT) [MAT-OPT] Optimisation [MAT-88.105-SG] M.Sc. Mathematics [NORM] Active

## Courses

Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
4V+2U MAT-52-16-K-7
Robust Optimization
P 84 h 186 h - - PL1 9.0 irreg.
• About [MAT-52-16-K-7]: Title: "Robust Optimization"; Presence-Time: 84 h; Self-Study: 186 h

## Examination achievement PL1

• Form of examination: oral examination (20-30 Min.)
• Examination Frequency: irregular (by arrangement)
• Examination number: 86387 ("Robust Optimization")

## Contents

• modelling with robust optimization,
• modelling and concepts of uncertainty set,
• model reformulations in solvable problems.
• problem complexities,
• linear, non-linear and integer optimization in robust optimization,
• application to combinational problems,
• approaches from robust optimization: Soyster approach for uncertain problems; strict robustness; robust regularization; minimax regret approach; adjustable robustness; approach by Bertsimas and Sim; recoverable robustness.

## Competencies / intended learning achievements

Upon successful completion of this module, the students are familiar with different methods to solve and model the uncertainty in optimization. They know and understand the complexities of the approaches and are able to solve the problems with the help of specific algorithms. In particular, for problems with a suitable structure, they are able to construct reformulations as non-uncertain optimization problems. Moreover, they can critically assess the possibilities and limitations of the use of the algorithms. They understand the proofs presented in the lecture and are able to reproduce and explain them.

In the exercise classes, the students have deepened their knowledge and gained a skilled, precise and independent handling of the terms, propositions and methods taught in the lecture. Moreover, they have learned to apply algorithms and models to practical problems by the use of appropriate, higher programming languages and MIP solvers.

## Literature

• A. Ben-Tal, L. El Ghaoui, A. Nemirovski: Robust Optimization,
• P. Kouvelis, G. Yu: Robust Discrete Optimization and Its Applications.

None

## References to Module / Module Number [MAT-52-16-M-7]

Module-Pool Name
[MAT-52-MPOOL-7] Specialisation Mathematical Optimisation (M.Sc.)
[MAT-AM-MPOOL-7] Applied Mathematics (Advanced Modules M.Sc.)