National Repository of Grey Literature 2 records found  Search took 0.00 seconds. 
Solving methods for bilevel optimization problems
Lžičař, Jiří ; Kopa, Miloš (advisor) ; Branda, Martin (referee)
The presented thesis discusses bilevel programming problems with the focus on solution algorithms. Bilevel programming problem is a hierarchical programming problem, where constraints contain another programming problem. We formulate basic bilevel optimization theory and describe three types of so- lution algorithms for bilevel programming problems: Algorithms based on KKT reformulation where the lower level is replaced by its KKT conditions, algorithms based on optimal value function where the bilevel programming problem is re- duced to a single level problem using the optimal value function of the lower level problem, and algorithms solving linear bilevel programming problems. Using real data for portfolio optimization bilevel programming problems, we compare ability to solve the problems and computing time of some of the pre- sented algorithms. 1
Characterization of convex sets
Lžičař, Jiří ; Lachout, Petr (advisor) ; Kozmík, Václav (referee)
The idea of convexity is very important especially for probability theory, optimization and stochastic optimization. Convexity is a unique set pro- perty in many ways, which is worth to be studied. Various properties of convex sets are generally known, such as the ones related to separability. It however becomes apparent that the definition of convexity is very interesting, since it is possible to replace the definition by various collections of properties which are equivalent to it. There also exist set operations preserving convexity and another ones which preserve it when supported by another requirements. 1

See also: similar author names
4 Lžičař, Jakub
2 Lžičař, Jan
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