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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
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Alternative economies in rural Russia
Vargolskaia, Virginia ; Stöckelová, Tereza (advisor) ; Abu Ghosh, Yasar (referee)
The aim of this diploma thesis is to study how nonhuman agents are introduced and employed as a replacement for social reproduction by analyzing the environment and types of exchange practiced in the countryside of post-socialist Russia. The farm where my fieldwork took place exhibits many types of exchange, among which cryptocurrencies, seen as a socio- material algorithm, are used for the redistribution of essential goods and/or favors in a method similar to those used in former socialist and post-socialist economies. Drawing from the anthropological discussion on gift-commodity logic in the area, I look at cryptocurrencies as a hybrid - they hold the qualities of a gift (authority, name) and could be used to speculate with on the crypto stock-exchange (commodity). Key words: alternative economies, post-socialism, cryptocurrencies, algorithms, sociomateriality
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Line search in descent methods
Moravová, Adéla ; Tichý, Petr (advisor) ; Vlasák, Miloslav (referee)
In this thesis, we deal with descent methods for functional minimalization. We discuss three conditions for the choice of the step length (Armijo, Goldstein, and Wolfe condition) and four descent methods (The steepest descent method, Newton's method, Quasi-Newton's method BFGS and the conjugate gradient method). We discuss their convergence properties and their advantages and dis- advantages. Finally, we test these methods numerically in the GNU Octave pro- gramming system on three different functions with different number of variables. 1
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Algorithms for Automatic Image Cropping
Ambrož, Vít ; Brejcha, Jan (referee) ; Čadík, Martin (advisor)
The main goal of this bachelor thesis is study and implementation of methods that can automatically crop images, so the result has good usability from a photographic view. In this thesis are made experiments with three methods and possible optimalizations are discussed. The properties of cropping algorithms are also described here and the evaluation of implemented algoritmhs is made according to user testing.
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Navigation in Public Transport
Turic, Matúš ; Křivka, Zbyněk (referee) ; Burget, Radek (advisor)
This master's thesis deals with the issue of traveling in public transport. In the first part the author informs about similar applications and theories necessary for understanding the problems. In the second part, the author describes the design and behavior of the mobile and server application, including the used technologies. Created mobile application has the task of navigating the user from one point to another in the shortest possible time, while it should be possible to replace the current route with faster one.
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Historical development of numerical methods and computational techniques, from the perspective of mathematics education in elementary school.
DIVÍŠKOVÁ, Michaela
In my diploma thesis I deal with historical numerical procedures and their application in teaching. In a total of eight chapters, I describe counting techniques from history, such as magic squares, interesting counting algorithms, unconventional divisibility criteria, ancient numeration techniques, golden ratio, figurate numbers, and graphic papers. I deal with the use of historical numerical methods in teaching in the final chapter. This chapter contains eight worksheets and activity suggestions with methodical commentary.
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Adaptive Blind Separation of Instantaneous Linear Mixtures of Independent Sources
Šembera, Ondřej ; Tichavský, Petr ; Koldovský, Zbyněk
In many applications, there is a need to blindly separate independent sources from their linear instantaneous mixtures while the mixing matrix or source properties are slowly or abruptly changing in time. The easiest way to separate the data is to consider off-line estimation of the model parameters repeatedly in time shifting window. Another popular method is the stochastic natural gradient algorithm, which relies on non-Gaussianity of the separated signals and is adaptive by its nature. In this paper, we propose an adaptive version of two blind source separation algorithms which exploit non-stationarity of the original signals. The results indicate that the proposed algorithms slightly outperform the natural gradient in the trade-off between the algorithm’s ability to quickly adapt to changes in the mixing matrix and the variance of the estimate when the mixing is stationary.
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Computational Bounded Rationality
Černý, Jakub ; Loebl, Martin (advisor) ; Hladík, Milan (referee)
This thesis formalizes a model of bounded rationality in extensive-form games called game-playing schemata. In this model, the strategies are repre- sented by a structure consisting of a deterministic finite automaton and two computational functions. The automaton represents a structured memory of the player, while the functions represent the ability of the player to identify efficient abstractions of the game. Together, the schema is a realization of a pure strategy which can be implemented by a player in order to play a given game. The thesis shows how to construct correctly playing schema for every pure strategy in any multi-player extensive-form game with perfect recall and how to evaluate its complexity. It proves that equilibria in schemata strategies always exist and computing them is PPAD-hard. Moreover, for a class of efficiently representable strategies, computing MAXPAY-EFCE can be done in polynomial time. 1
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