Approximation and Optimization
Approximation and Optimization

Author: Ioannis C. Demetriou

Publisher: Springer

Published: 2019-05-10

Total Pages: 237

ISBN-13: 3030127672

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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.

Optimization and Approximation
Optimization and Approximation

Author: Pablo Pedregal

Publisher: Springer

Published: 2017-09-07

Total Pages: 261

ISBN-13: 3319648438

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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.

Complexity and Approximation
Complexity and Approximation

Author: Giorgio Ausiello

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 536

ISBN-13: 3642584128

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This book documents the state of the art in combinatorial optimization, presenting approximate solutions of virtually all relevant classes of NP-hard optimization problems. The wealth of problems, algorithms, results, and techniques make it an indispensible source of reference for professionals. The text smoothly integrates numerous illustrations, examples, and exercises.

Approximation and Optimization of Discrete and Differential Inclusions
Approximation and Optimization of Discrete and Differential Inclusions

Author: Elimhan N Mahmudov

Publisher: Elsevier

Published: 2011-08-25

Total Pages: 396

ISBN-13: 0123884284

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Optimal control theory has numerous applications in both science and engineering. This book presents basic concepts and principles of mathematical programming in terms of set-valued analysis and develops a comprehensive optimality theory of problems described by ordinary and partial differential inclusions. In addition to including well-recognized results of variational analysis and optimization, the book includes a number of new and important ones Includes practical examples

Approximation Methods in Optimization of Nonlinear Systems
Approximation Methods in Optimization of Nonlinear Systems

Author: Peter I. Kogut

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2019-12-02

Total Pages: 351

ISBN-13: 3110668521

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The monograph addresses some problems particularly with regard to ill-posedness of boundary value problems and problems where we cannot expect to have uniqueness of their solutions in the standard functional spaces. Bringing original and previous results together, it tackles computational challenges by exploiting methods of approximation and asymptotic analysis and harnessing differences between optimal control problems and their underlying PDEs

Approximation Theory and Optimization
Approximation Theory and Optimization

Author: M. D. Buhmann

Publisher: Cambridge University Press

Published: 1997-11-13

Total Pages: 238

ISBN-13: 9780521581905

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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.

Approximation Algorithms and Semidefinite Programming
Approximation Algorithms and Semidefinite Programming

Author: Bernd Gärtner

Publisher: Springer Science & Business Media

Published: 2012-01-10

Total Pages: 253

ISBN-13: 3642220150

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Semidefinite programs constitute one of the largest classes of optimization problems that can be solved with reasonable efficiency - both in theory and practice. They play a key role in a variety of research areas, such as combinatorial optimization, approximation algorithms, computational complexity, graph theory, geometry, real algebraic geometry and quantum computing. This book is an introduction to selected aspects of semidefinite programming and its use in approximation algorithms. It covers the basics but also a significant amount of recent and more advanced material. There are many computational problems, such as MAXCUT, for which one cannot reasonably expect to obtain an exact solution efficiently, and in such case, one has to settle for approximate solutions. For MAXCUT and its relatives, exciting recent results suggest that semidefinite programming is probably the ultimate tool. Indeed, assuming the Unique Games Conjecture, a plausible but as yet unproven hypothesis, it was shown that for these problems, known algorithms based on semidefinite programming deliver the best possible approximation ratios among all polynomial-time algorithms. This book follows the “semidefinite side” of these developments, presenting some of the main ideas behind approximation algorithms based on semidefinite programming. It develops the basic theory of semidefinite programming, presents one of the known efficient algorithms in detail, and describes the principles of some others. It also includes applications, focusing on approximation algorithms.

The Design of Approximation Algorithms
The Design of Approximation Algorithms

Author: David P. Williamson

Publisher: Cambridge University Press

Published: 2011-04-26

Total Pages: 518

ISBN-13: 9780521195270

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Discrete optimization problems are everywhere, from traditional operations research planning problems, such as scheduling, facility location, and network design; to computer science problems in databases; to advertising issues in viral marketing. Yet most such problems are NP-hard. Thus unless P = NP, there are no efficient algorithms to find optimal solutions to such problems. 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 part of the book is devoted to a single algorithmic technique, which is then applied to several different problems. The second part revisits the techniques but offers more sophisticated treatments of them. The book also covers methods for proving that optimization problems are hard to approximate. Designed as a textbook for graduate-level algorithms courses, the book will also serve as a reference for researchers interested in the heuristic solution of discrete optimization problems.