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Optimization in Financial Applications
Večeřa, Tomáš ; Cabalka, Matouš (referee) ; Popela, Pavel (advisor)
The main purpose of this thesis is to create an efficient stock portfolio, specifically to optimize current distribution of stock index S&P 500. The building process consist of well-established mathematical-economical methods, which are then improved by applying mathematical models from statistics and optimization. Firstly, we define essential terms in order to reach deeper understanding of used methods. Afterwards, process of thorough selection of stocks and sectors comes to place. Data are then processed in program GAMS in three different ways, depending on investors preference. Although this approach was applied to current era, its principles are applicable to any given timeline.
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Budget Optimization
Golasowski, Martin ; Janíček, Ladislav (referee) ; Popela, Pavel (advisor)
The bachelor's thesis aims to approach the issue of creating a budget for a public university and the subsequent creation of a mathematical model. The thesis explains the rules and formulas for the distribution of funds for higher education to individual universities. Then, the formulas for the redistribution of these funds between individual faculties are given. Subsequently, a mathematical model of nonlinear programming in the GAMS system is built using real data and constraints. The model is then used to examine the change in the distribution of funds for various objective functions. The aim of compiling the model was not to offer a tool that will be automatically used for the distribution of funds at BUT, but to provide its users with a wider range of computational experiments and gain better insight into the problem.
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Exact penalization in optimization
Šešulka, Marek ; Branda, Martin (advisor) ; Kopa, Miloš (referee)
This thesis deals with one of the possible different approaches to solving nonlinear optimization problems by convertion to finding non-bounded extrema of function, where constrains are transfered to objective function via penalty function. We will introduce exterior penalty function method and appropriate algorithm for solving this type for problems. The thesis also deals with exact penalty functions, which do not requires limit approximation of the penalty pa- rameter to infinity. Then we deal with integer binary nonlinear progamming, where several suitable penalty functions are presented to solve this type of pro- blem. In the numerical part, the thesis deals with the minimization of risk at the specifed minimum expected return on the sparse portfolio. We observe the effect of changing the penalty parameter on the results of ten different minimization problems calculating risk of sparsity portfolios. 1
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ADVANCED REGRESSION MODELS
Rosecký, Martin ; Popela, Pavel (referee) ; Bednář, Josef (advisor)
This thesis summarizes latest findings about municipal solid waste (MSW) modelling. These are used to solve multivariable version of inverse prediction problem. It is not possible to solve such problem analytically, so heuristic framework using regression models and data reconciliation was developed. As a side product, models for MSW modelling using PCA (Principal Component Analysis) and LM (Linear Model) were created. These were compared with heuristic model called RF (Random Forest). Both of these models were also used for per capita MSW modelling. Theoretical parts about generalized linear models, data reconciliation and nonlinear programming are also included.
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Mathematical Programming Models for Optimal Control Problems
Dražka, Jan ; Mrázková, Eva (referee) ; Popela, Pavel (advisor)
This thesis deals with optimization of a vehicle’s (racing) drive on a track. The model of a vehicle and a track is built in this thesis. The first chapter is devoted to the fastest pass problem formulation. The problem optimizes (in the least time) the vehicle’s drive from a start line to a finish line. The problem is formulated as an optimal control theory problem. In the second chapter the optimal control theory problem is suitably discretised and transformed into a nonlinear programming problem. The transformation of the fastest pass problem into nonlinear programming problem, its detailed and illustrative derivation and reformulation form the main part of the thesis. Third chapter presents the implementation and solution of the problem using GAMS and MATLAB. This thesis is a part of a specific research project on which the author has participated. The main contribution of the author is an original formulation of the fastest pass problem as a nonlinear programming problem and its implementation and solving using GAMS.
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Mathematical Model for Faculty Budget
Holá, Lucie ; Roupec, Jan (referee) ; Popela, Pavel (advisor)
The idea of this diploma thesis is an origin application of optimization models to solve a wage funds allocation problem on various institutes of each faculty. This diploma thesis includes an outline of linear programming models, nonlinear programming models, multiply programming models and parametric programming models. Studied questions are debating in wider context of distributing financial resources from the Budget of the Czech republic, through Ministry of education, youth and sports, universities, faculties after as much as various institutes. The accent is given on question of definition assessment scales of achievement criteria with general-purpose kvantification.
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Process Optimization
Vilém, Jan ; Hrabec, Dušan (referee) ; Popela, Pavel (advisor)
This bachelor's thesis examine the problem of the process optimization in mechanical engineering. It contains optimization model to optimize cutting conditions in turning. The problem was programmed in the GAMS system as linear and nonlinear problem. Limiting conditions are generally defined for several types of technological processes.
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