Linear Optimization And Approximation

Author : K. Glashoff,S.-A. Gustafson
Publisher : Springer Science & Business Media
Page : 209 pages
File Size : 43,7 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461211426

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Linear Optimization and Approximation by K. Glashoff,S.-A. Gustafson Pdf

A linear optimization problem is the task of minimizing a linear real-valued function of finitely many variables subject to linear con straints; in general there may be infinitely many constraints. This book is devoted to such problems. Their mathematical properties are investi gated and algorithms for their computational solution are presented. Applications are discussed in detail. Linear optimization problems are encountered in many areas of appli cations. They have therefore been subject to mathematical analysis for a long time. We mention here only two classical topics from this area: the so-called uniform approximation of functions which was used as a mathematical tool by Chebyshev in 1853 when he set out to design a crane, and the theory of systems of linear inequalities which has already been studied by Fourier in 1823. We will not treat the historical development of the theory of linear optimization in detail. However, we point out that the decisive break through occurred in the middle of this century. It was urged on by the need to solve complicated decision problems where the optimal deployment of military and civilian resources had to be determined. The availability of electronic computers also played an important role. The principal computational scheme for the solution of linear optimization problems, the simplex algorithm, was established by Dantzig about 1950. In addi tion, the fundamental theorems on such problems were rapidly developed, based on earlier published results on the properties of systems of linear inequalities.

Author : K Glashoff,S -A Gustafson
Publisher : Unknown
Page : 212 pages
File Size : 52,6 Mb
Release : 1983-04-13
Category : Electronic
ISBN : 1461211433

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Linear Optimization and Approximation by K Glashoff,S -A Gustafson Pdf

Author : Pablo Pedregal
Publisher : Springer
Page : 254 pages
File Size : 50,9 Mb
Release : 2017-09-07
Category : Mathematics
ISBN : 9783319648439

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Optimization and Approximation by Pablo Pedregal Pdf

This book provides a basic, initial resource, introducing science and engineering students to the field of optimization. It covers three main areas: mathematical programming, calculus of variations and optimal control, highlighting the ideas and concepts and offering insights into the importance of optimality conditions in each area. It also systematically presents affordable approximation methods. Exercises at various levels have been included to support the learning process.

Author : Ioannis C. Demetriou,Panos M. Pardalos
Publisher : Springer
Page : 237 pages
File Size : 48,8 Mb
Release : 2019-05-10
Category : Mathematics
ISBN : 9783030127671

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Approximation and Optimization by Ioannis C. Demetriou,Panos M. Pardalos Pdf

This book focuses on the development of approximation-related algorithms and their relevant applications. Individual contributions are written by leading experts and reflect emerging directions and connections in data approximation and optimization. Chapters discuss state of the art topics with highly relevant applications throughout science, engineering, technology and social sciences. Academics, researchers, data science practitioners, business analysts, social sciences investigators and graduate students will find the number of illustrations, applications, and examples provided useful. This volume is based on the conference Approximation and Optimization: Algorithms, Complexity, and Applications, which was held in the National and Kapodistrian University of Athens, Greece, June 29–30, 2017. The mix of survey and research content includes topics in approximations to discrete noisy data; binary sequences; design of networks and energy systems; fuzzy control; large scale optimization; noisy data; data-dependent approximation; networked control systems; machine learning ; optimal design; no free lunch theorem; non-linearly constrained optimization; spectroscopy.

Author : K. Glashoff,S.-A. Gustafson
Publisher : Springer
Page : 212 pages
File Size : 47,8 Mb
Release : 1983-04-13
Category : Science
ISBN : 0387908579

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Linear Optimization and Approximation by K. Glashoff,S.-A. Gustafson Pdf

A linear optimization problem is the task of minimizing a linear real-valued function of finitely many variables subject to linear con straints; in general there may be infinitely many constraints. This book is devoted to such problems. Their mathematical properties are investi gated and algorithms for their computational solution are presented. Applications are discussed in detail. Linear optimization problems are encountered in many areas of appli cations. They have therefore been subject to mathematical analysis for a long time. We mention here only two classical topics from this area: the so-called uniform approximation of functions which was used as a mathematical tool by Chebyshev in 1853 when he set out to design a crane, and the theory of systems of linear inequalities which has already been studied by Fourier in 1823. We will not treat the historical development of the theory of linear optimization in detail. However, we point out that the decisive break through occurred in the middle of this century. It was urged on by the need to solve complicated decision problems where the optimal deployment of military and civilian resources had to be determined. The availability of electronic computers also played an important role. The principal computational scheme for the solution of linear optimization problems, the simplex algorithm, was established by Dantzig about 1950. In addi tion, the fundamental theorems on such problems were rapidly developed, based on earlier published results on the properties of systems of linear inequalities.

Author : Ding-Zhu Du,Jie Sun
Publisher : Springer Science & Business Media
Page : 402 pages
File Size : 43,9 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461336297

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Advances in Optimization and Approximation by Ding-Zhu Du,Jie Sun Pdf

This book is a collection of research papers in optimization and approximation dedicated to Professor Minyi Yue of the Institute of Applied Mathematics, Beijing, China. The papers provide a broad spectrum of research on optimization problems, including scheduling, location, assignment, linear and nonlinear programming problems as well as problems in molecular biology. The emphasis of the book is on algorithmic aspects of research work in optimization. Special attention is paid to approximation algorithms, including heuristics for combinatorial approximation problems, approximation algorithms for global optimization problems, and applications of approximations in real problems. The work provides the state of the art for researchers in mathematical programming, operations research, theoretical computer science and applied mathematics.

Author : Nabih Abdelmalek,William A. Malek
Publisher : CRC Press
Page : 964 pages
File Size : 50,6 Mb
Release : 2008-05-19
Category : Mathematics
ISBN : 9781584889786

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Numerical Linear Approximation in C by Nabih Abdelmalek,William A. Malek Pdf

Illustrating the relevance of linear approximation in a variety of fields, Numerical Linear Approximation in C presents a unique collection of linear approximation algorithms that can be used to analyze, model, and compress discrete data. Developed by the lead author, the algorithms have been successfully applied to several engineering projects at the National Research Council of Canada. Basing most of the algorithms on linear programming techniques, the book begins with an introductory section that covers applications, the simplex method, and matrices. The next three parts focus on various L1, Chebyshev, and least squares approximations, including one-sided, bounded variables, and piecewise. The final section presents the solution of underdetermined systems of consistent linear equations that are subject to different constraints on the elements of the unknown solution vector. Except in the preliminary section, all chapters include the C functions of the algorithms, along with drivers that contain numerous test case examples and results. The accompanying CD-ROM also provides the algorithms written in C code as well as the test drivers. To use the software, it is not required to understand the theory behind each function.

Author : M. D. Buhmann,A. Iserles
Publisher : Cambridge University Press
Page : 238 pages
File Size : 51,7 Mb
Release : 1997-11-13
Category : Mathematics
ISBN : 0521581907

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Approximation Theory and Optimization by M. D. Buhmann,A. Iserles Pdf

Michael Powell is one of the world's foremost figures in numerical analysis. This volume, first published in 1997, is derived from invited talks given at a meeting celebrating his 60th birthday and, reflecting Powell's own achievements, focuses on innovative work in optimisation and in approximation theory. The individual papers have been written by leading authorities in their subjects and are a mix of expository articles and surveys. They have all been reviewed and edited to form a coherent volume for this important discipline within mathematics, with highly relevant applications throughout science and engineering.

Author : Michael C. Ferris,Olvi L. Mangasarian,Stephen J. Wright
Publisher : SIAM
Page : 277 pages
File Size : 46,6 Mb
Release : 2007-01-01
Category : Mathematics
ISBN : 0898718775

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Linear Programming with MATLAB by Michael C. Ferris,Olvi L. Mangasarian,Stephen J. Wright Pdf

This textbook provides a self-contained introduction to linear programming using MATLAB software to elucidate the development of algorithms and theory. Early chapters cover linear algebra basics, the simplex method, duality, the solving of large linear problems, sensitivity analysis, and parametric linear programming. In later chapters, the authors discuss quadratic programming, linear complementarity, interior-point methods, and selected applications of linear programming to approximation and classification problems. Exercises are interwoven with the theory presented in each chapter, and two appendices provide additional information on linear algebra, convexity, nonlinear functions, and on available MATLAB commands, respectively. Readers can access MATLAB codes and associated mex files at a Web site maintained by the authors. Only a basic knowledge of linear algebra and calculus is required to understand this textbook, which is geared toward junior and senior-level undergraduate students, first-year graduate students, and researchers unfamiliar with linear programming.

Author : Werner Krabs
Publisher : John Wiley & Sons
Page : 240 pages
File Size : 41,9 Mb
Release : 1979
Category : Mathematics
ISBN : UOM:39015017334700

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Optimization and Approximation by Werner Krabs Pdf

Author : David P. Williamson,David B. Shmoys
Publisher : Cambridge University Press
Page : 517 pages
File Size : 52,8 Mb
Release : 2011-04-26
Category : Computers
ISBN : 9781139498173

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The Design of Approximation Algorithms by David P. Williamson,David B. Shmoys Pdf

Discrete optimization problems are everywhere, from traditional operations research planning (scheduling, facility location and network design); to computer science databases; to advertising issues in viral marketing. Yet most such problems are NP-hard; unless P = NP, there are no efficient algorithms to find optimal solutions. This book shows how to design approximation algorithms: efficient algorithms that find provably near-optimal solutions. The book is organized around central algorithmic techniques for designing approximation algorithms, including greedy and local search algorithms, dynamic programming, linear and semidefinite programming, and randomization. Each chapter in the first section is devoted to a single algorithmic technique applied to several different problems, with more sophisticated treatment in the second section. The book also covers methods for proving that optimization problems are hard to approximate. Designed as a textbook for graduate-level algorithm courses, it will also serve as a reference for researchers interested in the heuristic solution of discrete optimization problems.

Author : Panos M. Pardalos
Publisher : World Scientific
Page : 536 pages
File Size : 42,6 Mb
Release : 1993
Category : Mathematics
ISBN : 9810214154

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Complexity in Numerical Optimization by Panos M. Pardalos Pdf

Computational complexity, originated from the interactions between computer science and numerical optimization, is one of the major theories that have revolutionized the approach to solving optimization problems and to analyzing their intrinsic difficulty.The main focus of complexity is the study of whether existing algorithms are efficient for the solution of problems, and which problems are likely to be tractable.The quest for developing efficient algorithms leads also to elegant general approaches for solving optimization problems, and reveals surprising connections among problems and their solutions.This book is a collection of articles on recent complexity developments in numerical optimization. The topics covered include complexity of approximation algorithms, new polynomial time algorithms for convex quadratic minimization, interior point algorithms, complexity issues regarding test generation of NP-hard problems, complexity of scheduling problems, min-max, fractional combinatorial optimization, fixed point computations and network flow problems.The collection of articles provide a broad spectrum of the direction in which research is going and help to elucidate the nature of computational complexity in optimization. The book will be a valuable source of information to faculty, students and researchers in numerical optimization and related areas.

Author : Stephen P. Boyd,Lieven Vandenberghe
Publisher : Cambridge University Press
Page : 744 pages
File Size : 41,8 Mb
Release : 2004-03-08
Category : Business & Economics
ISBN : 0521833787

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Convex Optimization by Stephen P. Boyd,Lieven Vandenberghe Pdf

Convex optimization problems arise frequently in many different fields. This book provides a comprehensive introduction to the subject, and shows in detail how such problems can be solved numerically with great efficiency. The book begins with the basic elements of convex sets and functions, and then describes various classes of convex optimization problems. Duality and approximation techniques are then covered, as are statistical estimation techniques. Various geometrical problems are then presented, and there is detailed discussion of unconstrained and constrained minimization problems, and interior-point methods. The focus of the book is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. It contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance and economics.

Author : Zhening Li,Simai He,Shuzhong Zhang
Publisher : Springer Science & Business Media
Page : 124 pages
File Size : 52,6 Mb
Release : 2012-07-25
Category : Mathematics
ISBN : 9781461439844

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Approximation Methods for Polynomial Optimization by Zhening Li,Simai He,Shuzhong Zhang Pdf

Polynomial optimization have been a hot research topic for the past few years and its applications range from Operations Research, biomedical engineering, investment science, to quantum mechanics, linear algebra, and signal processing, among many others. In this brief the authors discuss some important subclasses of polynomial optimization models arising from various applications, with a focus on approximations algorithms with guaranteed worst case performance analysis. The brief presents a clear view of the basic ideas underlying the design of such algorithms and the benefits are highlighted by illustrative examples showing the possible applications. This timely treatise will appeal to researchers and graduate students in the fields of optimization, computational mathematics, Operations Research, industrial engineering, and computer science.

Author : Daniel Bienstock
Publisher : Springer
Page : 111 pages
File Size : 45,8 Mb
Release : 2013-03-26
Category : Mathematics
ISBN : 1475776713

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Potential Function Methods for Approximately Solving Linear Programming Problems: Theory and Practice by Daniel Bienstock Pdf

Potential Function Methods For Approximately Solving Linear Programming Problems breaks new ground in linear programming theory. The book draws on the research developments in three broad areas: linear and integer programming, numerical analysis, and the computational architectures which enable speedy, high-level algorithm design. During the last ten years, a new body of research within the field of optimization research has emerged, which seeks to develop good approximation algorithms for classes of linear programming problems. This work both has roots in fundamental areas of mathematical programming and is also framed in the context of the modern theory of algorithms. The result of this work, in which Daniel Bienstock has been very much involved, has been a family of algorithms with solid theoretical foundations and with growing experimental success. This book will examine these algorithms, starting with some of the very earliest examples, and through the latest theoretical and computational developments.