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In this Master Thesis is investigated several optimization techniques in the context of automatizing the Machine Learning Pipeline. The goal is to use these techniques to find the best set of features together with best model with the best hyperparameters values. The performance of the techniques are compared on various tasks.
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Linear programming attracted the interest of mathematicians during and after World War II when the first computers were constructed and methods for solving large linear programming problems were sought in connection with specific practical problems—for example, providing logistical support for the U.S. Armed Forces or modeling national economies. Early attempts to apply linear programming methods to solve practical problems failed to satisfy expectations. There were various reasons for the failure. One of them, which is the central topic of this book, was the inexactness of the data used to create the models. This phenomenon, inherent in most practical problems, has been dealt with in several ways. At first, linear programming models used "average” values of inherently vague coefficients, but the optimal solutions of these models were not always optimal for the original problem itself. Later researchers developed the stochastic linear programming approach, but this too has its limitations. Recently, interest has been given to linear programming problems with data given as intervals, convex sets and/or fuzzy sets. The individual results of these studies have been promising, but the literature has not presented a unified theory. Linear Optimization Problems with Inexact Data attempts to present a comprehensive treatment of linear optimization with inexact data, summarizing existing results and presenting new ones within a unifying framework. Audience This book is intended for postgraduate or graduate students in the areas of operations research, optimization theory, linear algebra, interval analysis, reliable computing, and fuzzy sets. The book will also be useful for researchers in these respective areas.
Linear programming. --- Mathematical optimization. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Production scheduling --- Programming (Mathematics)
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Invexity and Optimization presents results on invex function and their properties in smooth and nonsmooth cases, pseudolinearity and eta-pseudolinearity. Results on optimality and duality for a nonlinear scalar programming problem are presented, second and higher order duality results are given for a nonlinear scalar programming problem, and saddle point results are also presented. Invexity in multiobjective programming problems and Kuhn-Tucker optimality conditions are given for a multiobjecive programming problem, Wolfe and Mond-Weir type dual models are given for a multiobjective programming problem and usual duality results are presented in presence of invex functions. Continuous-time multiobjective problems are also discussed. Quadratic and fractional programming problems are given for invex functions. Symmetric duality results are also given for scalar and vector cases.
Mathematical optimization. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis
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This book opens new avenues in understanding mathematical models within the context of a transition economy. The exposition lays out the methods for combining different mathematical structures and tools to effectively build the next model that will accurately reflect real world economic processes. Mathematical modeling of weather phenomena allows us to forecast certain essential weather parameters without any possibility of changing them. By contrast, modeling of transition economies gives us the freedom to not only predict changes in important indexes of all types of economies, but also to influence them more effectively in the desired direction. Simply put: any economy, including a transitional one, can be controlled. This book is useful to anyone who wants to increase profits within their business, or improve the quality of their family life and the economic area they live in. It is beneficial for undergraduate and graduate students specializing in the fields of Economic Informatics, Economic Cybernetics, Applied Mathematics and Large Information Systems, as well as for professional economists, and employees of state planning and statistical organizations.
Economics --- Mathematical optimization. --- Mathematical models. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Economics, Mathematical --- Optimization.
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Operational research. Game theory --- Mathematical optimization --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Mathematical optimization.
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Introduction to sensitivity and stability analysis in nonlinear programming
Nonlinear programming. --- Mathematical optimization. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Programming (Mathematics) --- Nonlinear programming
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Operational research. Game theory --- Mathematical optimization. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Mathematical optimization
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Operational research. Game theory --- Mathematical optimization --- 519.6 --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis
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