Mathematical Theory Of Optimization
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Mathematical Theory Of Optimization
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Author : Ding-Zhu Du
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-10-31
Mathematical Theory Of Optimization written by Ding-Zhu Du and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-10-31 with Computers categories.
This book provides an introduction to the mathematical theory of optimization. It emphasizes the convergence theory of nonlinear optimization algorithms and applications of nonlinear optimization to combinatorial optimization. Mathematical Theory of Optimization includes recent developments in global convergence, the Powell conjecture, semidefinite programming, and relaxation techniques for designs of approximation solutions of combinatorial optimization problems.
Mathematical Theory Of Optimization
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Author : Ding-Zhu Du
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Mathematical Theory Of Optimization written by Ding-Zhu Du and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
Optimization is of central importance in all sciences. Nature inherently seeks optimal solutions. For example, light travels through the "shortest" path and the folded state of a protein corresponds to the structure with the "minimum" potential energy. In combinatorial optimization, there are numerous computationally hard problems arising in real world applications, such as floorplanning in VLSI designs and Steiner trees in communication networks. For these problems, the exact optimal solution is not currently real-time computable. One usually computes an approximate solution with various kinds of heuristics. Recently, many approaches have been developed that link the discrete space of combinatorial optimization to the continuous space of nonlinear optimization through geometric, analytic, and algebraic techniques. Many researchers have found that such approaches lead to very fast and efficient heuristics for solving large problems. Although almost all such heuristics work well in practice there is no solid theoretical analysis, except Karmakar's algorithm for linear programming. With this situation in mind, we decided to teach a seminar on nonlinear optimization with emphasis on its mathematical foundations. This book is the result of that seminar. During the last decades many textbooks and monographs in nonlinear optimization have been published. Why should we write this new one? What is the difference of this book from the others? The motivation for writing this book originated from our efforts to select a textbook for a graduate seminar with focus on the mathematical foundations of optimization.
Optimization Theory For Large Systems
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Author : Leon S. Lasdon
language : en
Publisher: Courier Corporation
Release Date : 2013-01-17
Optimization Theory For Large Systems written by Leon S. Lasdon and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-17 with Mathematics categories.
Important text examines most significant algorithms for optimizing large systems and clarifying relations between optimization procedures. Much data appear as charts and graphs and will be highly valuable to readers in selecting a method and estimating computer time and cost in problem-solving. Initial chapter on linear and nonlinear programming presents all necessary background for subjects covered in rest of book. Second chapter illustrates how large-scale mathematical programs arise from real-world problems. Appendixes. List of Symbols.
Mathematical Optimization And Economic Theory
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Author : Michael D. Intriligator
language : en
Publisher: SIAM
Release Date : 2002-01-01
Mathematical Optimization And Economic Theory written by Michael D. Intriligator and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-01-01 with Mathematics categories.
A classic account of mathematical programming and control techniques and their applications to static and dynamic problems in economics.
Optimization Theory And Practice
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Author : Wilhelm Forst
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-07-16
Optimization Theory And Practice written by Wilhelm Forst and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-16 with Mathematics categories.
Optimization is a field important in its own right but is also integral to numerous applied sciences, including operations research, management science, economics, finance and all branches of mathematics-oriented engineering. Constrained optimization models are one of the most widely used mathematical models in operations research and management science. This book gives a modern and well-balanced presentation of the subject, focusing on theory but also including algorithims and examples from various real-world applications. Detailed examples and counter-examples are provided--as are exercises, solutions and helpful hints, and Matlab/Maple supplements.
Entropy Optimization And Mathematical Programming
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Author : Shu-Cherng Fang
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-07-31
Entropy Optimization And Mathematical Programming written by Shu-Cherng Fang and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-07-31 with Business & Economics categories.
Entropy optimization is a useful combination of classical engineering theory (entropy) with mathematical optimization. The resulting entropy optimization models have proved their usefulness with successful applications in areas such as image reconstruction, pattern recognition, statistical inference, queuing theory, spectral analysis, statistical mechanics, transportation planning, urban and regional planning, input-output analysis, portfolio investment, information analysis, and linear and nonlinear programming. While entropy optimization has been used in different fields, a good number of applicable solution methods have been loosely constructed without sufficient mathematical treatment. A systematic presentation with proper mathematical treatment of this material is needed by practitioners and researchers alike in all application areas. The purpose of this book is to meet this need. Entropy Optimization and Mathematical Programming offers perspectives that meet the needs of diverse user communities so that the users can apply entropy optimization techniques with complete comfort and ease. With this consideration, the authors focus on the entropy optimization problems in finite dimensional Euclidean space such that only some basic familiarity with optimization is required of the reader.
Practical Mathematical Optimization
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Author : Jan Snyman
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-11-29
Practical Mathematical Optimization written by Jan Snyman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-11-29 with Mathematics categories.
This book presents basic optimization principles and gradient-based algorithms to a general audience, in a brief and easy-to-read form. It enables professionals to apply optimization theory to engineering, physics, chemistry, or business economics.
Mathematical Optimization And Economic Analysis
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Author : Mikulás Luptácik
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-10-03
Mathematical Optimization And Economic Analysis written by Mikulás Luptácik and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-10-03 with Mathematics categories.
"Mathematical Optimization and Economic Analysis" is a self-contained introduction to various optimization techniques used in economic modeling and analysis such as geometric, linear, and convex programming and data envelopment analysis. Through a systematic approach, this book demonstrates the usefulness of these mathematical tools in quantitative and qualitative economic analysis. The book presents specific examples to demonstrate each technique’s advantages and applicability as well as numerous applications of these techniques to industrial economics, regulatory economics, trade policy, economic sustainability, production planning, and environmental policy. Key Features include: - A detailed presentation of both single-objective and multiobjective optimization; - An in-depth exposition of various applied optimization problems; - Implementation of optimization tools to improve the accuracy of various economic models; - Extensive resources suggested for further reading. This book is intended for graduate and postgraduate students studying quantitative economics, as well as economics researchers and applied mathematicians. Requirements include a basic knowledge of calculus and linear algebra, and a familiarity with economic modeling.
Theory Of Vector Optimization
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Author : Dinh The Luc
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Theory Of Vector Optimization written by Dinh The Luc and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Business & Economics categories.
These notes grew out of a series of lectures given by the author at the Univer sity of Budapest during 1985-1986. Additional results have been included which were obtained while the author was at the University of Erlangen-Niirnberg under a grant of the Alexander von Humboldt Foundation. Vector optimization has two main sources coming from economic equilibrium and welfare theories of Edgeworth (1881) and Pareto (1906) and from mathemat ical backgrounds of ordered spaces of Cantor (1897) and Hausdorff (1906). Later, game theory of Borel (1921) and von Neumann (1926) and production theory of Koopmans (1951) have also contributed to this area. However, only in the fifties, after the publication of Kuhn-Tucker's paper (1951) on the necessary and sufficient conditions for efficiency, and of Deubreu's paper (1954) on valuation equilibrium and Pareto optimum, has vector optimization been recognized as a mathematical discipline. The stretching development of this field began later in the seventies and eighties. Today there are a number of books on vector optimization. Most of them are concerned with the methodology and the applications. Few of them offer a systematic study of the theoretical aspects. The aim of these notes is to pro vide a unified background of vector optimization,with the emphasis on nonconvex problems in infinite dimensional spaces ordered by convex cones. The notes are arranged into six chapters. The first chapter presents prelim inary material.
Practical Mathematical Optimization
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Author : Jan A Snyman
language : en
Publisher: Springer
Release Date : 2018-05-14
Practical Mathematical Optimization written by Jan A Snyman and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-14 with Mathematics categories.
This book presents basic optimization principles and gradient-based algorithms to a general audience, in a brief and easy-to-read form. It enables professionals to apply optimization theory to engineering, physics, chemistry, or business economics.