Doctoral Thesis

Advanced Decomposition Methods in Stochastic Convex Optimization

Final Thesis 5.32 MB Summary of Thesis 2.36 MB

Author of thesis: Ing. Jakub Kůdela, Ph.D.

Acad. year: 2019/2020

Supervisor: RNDr. Pavel Popela, Ph.D.

Reviewer's: prof. Csaba Fabian, RNDr. Martin Šmíd, Ph.D.

Abstract:

When working with stochastic programming problems, we frequently encounter optimization problems that are too large to be processed by routine methods of mathematical programming. However, in some cases the problem structure allows for a use of specialized decomposition methods that (when utilizing said structure) can be employed to efficiently solve very large optimization problems. This work focuses on two classes of  stochastic programming problems that have an exploitable structure,
namely two-stage stochastic programming problems and chance constrained problems, and the advanced decomposition methods that can be used to solve optimization problems in these two classes. We describe a novel warm-start cuts for the Generalized Benders Decomposition, which is used as a methods for the two-stage stochastic programming problems. For the class of chance constraint problems, we introduce an original  decomposition method, that we named the Pool & Discard algorithm. The usefulness of the described decomposition methods is demonstrated
on several examples and engineering applications.

Keywords:

stochastic optimization, stochastic programming, decomposition methods, two-stage stochastic programming problems, chance constrained problems

Date of defence

20.9.2019

Result of the defence

Defended (thesis was successfully defended)

znakmkaPznamka

Process of defence

The dissertation contains interesting and original results and demonstrates up-todate knowledge in a wide range of areas. The desenbed procedness have been implemented and thoroughly tested. The implemented software tools have been successfully applied in the solution of real-life problems.

Language of thesis

English

Faculty

Department

Study field

Applied Mathematics

Composition of Committee

prof. RNDr. Miloslav Druckmüller, CSc. (předseda)
prof. Csaba Fabian (člen)
RNDr. Martin Šmíd, Ph.D. (člen)
prof. RNDr. Zdeněk Pospíšil, Ph.D. (člen)
assoc. prof. Francesca Maggioni (člen)
doc. RNDr. Miloš Kopa, Ph.D. (člen)
doc. RNDr. Martin Branda, Ph.D. (člen)
prof. RNDr. Jan Čermák, CSc. (člen)

Reviewer’s report
prof. Csaba Fabian

viz. posudek v pdf.
File inserted by the reviewer Size
Kudela report.pdf 184.9 kB

Reviewer’s report
RNDr. Martin Šmíd, Ph.D.

viz. posudek v pdf.
File inserted by the reviewer Size
kudela.pdf 109.18 kB