The topic of this thesis is bilevel optimization. Bilevel optimization problems are optimization problems where some variables in one optimization problem (the upper level problem) are constrained to be optimal in a second optimization problem (the lower level problem). Recent research has shown that several important problems in for example automatic control can be formulated as bilevel optimization problems. Unfortunately, the bilevel problems are known to often be very hard to solve in practice and the main focus in this thesis is therefore to investigate different algorithms to solve them efficiently. In the thesis, several common types of bilevel problems are discussed. Furthermore, different algorithms to solve these kinds of problems are compared theoretically. Finally, some promising ones are selected to be more thoroughly investigated in numerical experiments on a large number of randomly generated test problems with the purpose to evaluate the computational performance and reliability. In these experiments, bilevel problems with convex quadratic programming problems at the lower level and convex, as well as non-convex, quadratic programming problems at the upper level are considered. Finally, also an automatic control related problem is used as a benchmark problem.
author | = | {I. Rauov\'a}, |
title | = | {Evaluation of Different Bilevel Optimization Algorithms with Applications to Control}, |
school | = | {\'UIAM FCHPT STU v Bratislave}, |
year | = | {2010}, |
keyword | = | {bilevel optimization problems, global opimization}, |
address | = | {Radlinsk\'eho 9, 812 37 Bratislava}, |
month | = | {21. 05. 2010}, |
annote | = | {The topic of this thesis is bilevel optimization. Bilevel optimization problems are optimization problems where some variables in one optimization problem (the upper level problem) are constrained to be optimal in a\ second optimization problem (the lower level problem). Recent research has shown that several important problems in for example automatic control can be formulated as bilevel optimization problems. Unfortunately, the bilevel problems are known to often be very hard to solve in practice and the main focus in this thesis is therefore to investigate different algorithms to solve them efficiently. In the thesis, several common types of bilevel problems are discussed. Furthermore, different algorithms to solve these kinds of problems are compared theoretically. Finally, some promising ones are selected to be more thoroughly investigated in numerical experiments on a\ large number of randomly generated test problems with the purpose to evaluate the computational performance and reliability. In these experiments, bilevel problems with convex quadratic programming problems at the lower level and convex, as well as non-convex, quadratic programming problems at the upper level are considered. Finally, also an automatic control related problem is used as a\ benchmark problem.}, |
supervisor | = | {prof. Ing. Michal Kvasnica, PhD.}, |
url | = | {https://www.uiam.sk/assets/publication_info.php?id_pub=949} |