
Optimization problems with chance constraints
Drobný, Miloslav ; Adam, Lukáš (advisor) ; Lachout, Petr (referee)
Autor se v diplomové práci zabývá optimalizačními úlohami s pravděpodob nostními omezeními. Konkrétně pak situacemi, kdy není známo pravděpo dobnostní rozdělení přítomného náhodného efektu. K řešení těchto problém· lze přistoupit metodami optimistických a pesimistických scénář·, kdy z dané rodiny možných pravděpodobnostních rozdělení vybíráme bu¤ nejpříznivější možnou variantu, nebo naopak tu nejméně výhodnou. Optimalizační úlohy s pravděpodobnostními omezeními formulovanými pomocí výše zmíněných přístup· byly za učinění jistých předpoklad· transformovány do jednoduš ších a řešitelných optimalizačních úloh. Dosažené výsledky byly aplikovány na reálná data z oblastí optimalizace portfolia a zpracování obrazu. 1


Hierarchical Problems with Evolutionary Equilibrium Constraints
Adam, Lukáš ; Outrata, Jiří (advisor) ; Lachout, Petr (referee) ; Hoheisel, Tim (referee)
Title: Hierarchical Problems with Evolutionary Equilibrium Constraints Author: Lukáš Adam Supervisor: Prof. Jiří Outrata Abstract: In the presented thesis, we are interested in hierarchical models with evolutionary equilibrium constraints. Such models arise naturally when a timedependent problem is to be controlled or if parameters in such a model are to be identified. We intend to discretize the problem and solve it on the basis of the socalled implicit programming approach. This technique requires knowledge of a generalized derivative of the solution mapping which assigns the state variable to the control variable/parameter. The computation of this generalized derivative amounts equivalently to the computation of (limiting) normal cone to the graph of the solution mapping. In the first part we summarize known techniques for computation of the normal cone to the set which can be represented as a finite union of convex polyhedra. Then we propose a new approach based on the socalled normally admissible stratification and simplify the obtained formulas for the case of timedependent problems. The theoretical results are then applied first to deriving a criterion for the sensitivity analysis of the solution mapping and then to the solution of two practically motivated problems. The first one concerns optimal...


Management of the sports organisation FC Zličín and suggestions for improving it
Adam, Lukáš ; Ruda, Tomáš (advisor) ; Wroblowská, Zuzana (referee)
Title: Management of the sports organisation FC Zličín and suggestions for improving it Goals: The aim of this work, based on an analysis of managerial functions (planning, organizing, selection and deploying staff, leadership, control and some continuous functions), is to gather and subsequently process the proposals for improving the management of sports nonprofit organization Methods: Descriptive analysis, semistructured interview, SWOT analysis Results: The results of the work are proposals for change in the organizational structure of the sports club, modification and improvement of planning, promotional activities and sponsorship. Keywords: Managerial functions, nonprofit organization, civil association, society, management, footbal club


Learning newsboy
Hlubocký, Stanislav ; Lachout, Petr (advisor) ; Adam, Lukáš (referee)
Title: Learning Newsboy Author: Stanislav Hlubocký Department: Department of Probability and Mathematical Statistics Supervisor: doc. RNDr. Petr Lachout CSc. Department of Probability and Mathematical Statistics Abstract: The newsboy problem is a classical stochastic optimization program. The newsboy buys a bulk of papers and tries to sell them at a fixed higher price. The newspapers lose all value at the end of the day. In this thesis, different demands the newsboy can have and the strategies that result from their satisfying are analysed, including some generalised problems (Weather forecast, the flowergirl). All theoretical results and conjectures are tested using a simulation. Keywords: Newsboy, Flowergirl, simulation, Littlewood rule, Risk


Nash's equillibrium in a game of several players
Měsíček, Martin ; Lachout, Petr (advisor) ; Adam, Lukáš (referee)
This thesis is concerned with finding the Nash`s equilibrium in specific situations of card game poker texas holdem. It lays solid theoretical foundations illustrated on simple problems for understanding the notion of Nash`s equilibrium. Then we try to prove the existence of Nash`s equilibrium in the situations of two or more players in the game. It turns out that the twoplayer game can be represented by two person zerosum game and the game with more players by uncooperative game of N players. We describe a method for finding the Nash`s equilibrium for twoperson zerosum game game based on a method of solving problems of linear programming and we find the equilibrium for particular situations. Considering the extent of the problem, computing device is used when calculating some problems. Powered by TCPDF (www.tcpdf.org)


The core analysis of cooperative games
Kašpar, Martin ; Kopa, Miloš (advisor) ; Adam, Lukáš (referee)
In the present work we study theory of cooperative games and their solution. We assume that all players may form groups and cooperate, and we will try to find a solution, a rule how to divide the profit of the group among individual players. We will focus on a core of the game, its description, theoretical results and methods for analyzing its emptiness. We also investigate corecenter, which is one of the known options of choosing single profit division from the core. Then we will construct mathematical model of oligopoly together with method for counting characteristic function from real data. Finally, we apply the model on data from oil market. 1


Convexity in chance constraints programming
Olos, Marek ; Kopa, Miloš (advisor) ; Adam, Lukáš (referee)
This thesis deals with chance constrained stochastic programming pro blems. The first chapter is an introduction. We formulate several stochastic pro gramming problems in the second chapter. In chapter 3 we present the theory of αconcave functions and measures as a basic tool for proving convexity of the problems formulated in chapter 2 for the continuous distributions of the random vectors. We use the results of the theory to characterize a large class of the conti nuous distributions, that satisfy the sufficient conditions for the convexity and to prove convexity of concrete sets. In chapter 4 we present sufficient conditions for the convexity of the problems and we briefly discuss the method of the plevel ef ficient points. In chapter 5 we solve a portfolio selection problem using Kataoka's model. 1


Convexity in chance constraints programming
Olos, Marek ; Kopa, Miloš (advisor) ; Adam, Lukáš (referee)
1 Abstract: This thesis deals with chance constrained stochastic programming problems. We consider several chance constrained models and we focus on their convexity property. The thesis presents the theory of αconcave functions and measures as a basic tool for proving the convexity of the problems. We use the results of the theory to prove the convexity of the models first for the continu ous distributions, then for the discrete distributions of the random vectors. We characterize a large class of the continuous distributions, that satisfy the suffi cient conditions for the convexity of the given models and we present solving algorithms for these models. We present sufficient conditions for the convexity of the problems with dicrete distributions, too. We also deal with the algorithms for solving nonconvex problems and briefly discuss the difficulties that can occur when using these methods.

 
 