Complexity In Numerical Optimization

Author : Panos M. Pardalos
Publisher : World Scientific
Page : 536 pages
File Size : 51,5 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 : Panos M. Pardalos
Publisher : Springer Science & Business Media
Page : 597 pages
File Size : 51,9 Mb
Release : 2013-06-29
Category : Technology & Engineering
ISBN : 9781475731453

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Approximation and Complexity in Numerical Optimization by Panos M. Pardalos Pdf

There has been much recent progress in approximation algorithms for nonconvex continuous and discrete problems from both a theoretical and a practical perspective. In discrete (or combinatorial) optimization many approaches have been developed recently that link the discrete universe to the continuous universe through geomet ric, analytic, and algebraic techniques. Such techniques include global optimization formulations, semidefinite programming, and spectral theory. As a result new ap proximate algorithms have been discovered and many new computational approaches have been developed. Similarly, for many continuous nonconvex optimization prob lems, new approximate algorithms have been developed based on semidefinite pro gramming and new randomization techniques. On the other hand, computational complexity, originating from the interactions between computer science and numeri cal 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. A conference on Approximation and Complexity in Numerical Optimization: Con tinuous and Discrete Problems was held during February 28 to March 2, 1999 at the Center for Applied Optimization of the University of Florida.

Author : Ioannis C. Demetriou,Panos M. Pardalos
Publisher : Springer
Page : 237 pages
File Size : 42,7 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 : Coralia Cartis,Nicholas I. M. Gould,Philippe L. Toint
Publisher : SIAM
Page : 549 pages
File Size : 40,5 Mb
Release : 2022-07-06
Category : Mathematics
ISBN : 9781611976991

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Evaluation Complexity of Algorithms for Nonconvex Optimization by Coralia Cartis,Nicholas I. M. Gould,Philippe L. Toint Pdf

A popular way to assess the “effort” needed to solve a problem is to count how many evaluations of the problem functions (and their derivatives) are required. In many cases, this is often the dominating computational cost. Given an optimization problem satisfying reasonable assumptions—and given access to problem-function values and derivatives of various degrees—how many evaluations might be required to approximately solve the problem? Evaluation Complexity of Algorithms for Nonconvex Optimization: Theory, Computation, and Perspectives addresses this question for nonconvex optimization problems, those that may have local minimizers and appear most often in practice. This is the first book on complexity to cover topics such as composite and constrained optimization, derivative-free optimization, subproblem solution, and optimal (lower and sharpness) bounds for nonconvex problems. It is also the first to address the disadvantages of traditional optimality measures and propose useful surrogates leading to algorithms that compute approximate high-order critical points, and to compare traditional and new methods, highlighting the advantages of the latter from a complexity point of view. This is the go-to book for those interested in solving nonconvex optimization problems. It is suitable for advanced undergraduate and graduate students in courses on advanced numerical analysis, data science, numerical optimization, and approximation theory.

Author : Stephen A. Vavasis
Publisher : Oxford University Press, USA
Page : 192 pages
File Size : 54,7 Mb
Release : 1991
Category : Computers
ISBN : UOM:39015024818406

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Nonlinear Optimization by Stephen A. Vavasis Pdf

The fields of computer science and optimization greatly influence each other, and this book is about one important connection between the two: complexity theory. Complexity theory underlies computer algorithms and is used to address such questions as the efficiency of algorithms and the possibility of algorithmic solutions for particular problems. Furthermore, as optimization problems increase in size with hardware capacity, complexity theory plays a steadily growing role in the exploration of optimization algorithms. As larger and more complicated problems are addressed, it is more important than ever to understand the asymptotic complexity issues. This book describes some of the key developments in the complexity aspects of optimization during the last decade. It will be a valuable source of information for computer scientists and computational mathematicians.

Author : Christos H. Papadimitriou,Kenneth Steiglitz
Publisher : Courier Corporation
Page : 528 pages
File Size : 49,8 Mb
Release : 2013-04-26
Category : Mathematics
ISBN : 9780486320137

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Combinatorial Optimization by Christos H. Papadimitriou,Kenneth Steiglitz Pdf

This graduate-level text considers the Soviet ellipsoid algorithm for linear programming; efficient algorithms for network flow, matching, spanning trees, and matroids; the theory of NP-complete problems; local search heuristics for NP-complete problems, more. 1982 edition.

Author : Giorgio Ausiello,Pierluigi Crescenzi,Giorgio Gambosi,Viggo Kann,Alberto Marchetti-Spaccamela,Marco Protasi
Publisher : Springer Science & Business Media
Page : 536 pages
File Size : 51,5 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9783642584121

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Complexity and Approximation by Giorgio Ausiello,Pierluigi Crescenzi,Giorgio Gambosi,Viggo Kann,Alberto Marchetti-Spaccamela,Marco Protasi Pdf

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.

Author : Arkadiĭ Semenovich Nemirovskiĭ,David Berkovich I︠U︡din
Publisher : John Wiley & Sons
Page : 412 pages
File Size : 42,7 Mb
Release : 1983
Category : Programming (Mathematics).
ISBN : UOM:39015049375515

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Problem Complexity and Method Efficiency in Optimization by Arkadiĭ Semenovich Nemirovskiĭ,David Berkovich I︠U︡din Pdf

Author : Joseph-Frédéric Bonnans,Jean Charles Gilbert,Claude Lemarechal,Claudia A. Sagastizábal
Publisher : Springer Science & Business Media
Page : 421 pages
File Size : 55,9 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9783662050781

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Numerical Optimization by Joseph-Frédéric Bonnans,Jean Charles Gilbert,Claude Lemarechal,Claudia A. Sagastizábal Pdf

This book starts with illustrations of the ubiquitous character of optimization, and describes numerical algorithms in a tutorial way. It covers fundamental algorithms as well as more specialized and advanced topics for unconstrained and constrained problems. This new edition contains computational exercises in the form of case studies which help understanding optimization methods beyond their theoretical description when coming to actual implementation.

Author : Sergiy Butenko,Panos M. Pardalos
Publisher : CRC Press
Page : 415 pages
File Size : 42,9 Mb
Release : 2014-03-11
Category : Business & Economics
ISBN : 9781466577770

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Numerical Methods and Optimization by Sergiy Butenko,Panos M. Pardalos Pdf

For students in industrial and systems engineering (ISE) and operations research (OR) to understand optimization at an advanced level, they must first grasp the analysis of algorithms, computational complexity, and other concepts and modern developments in numerical methods. Satisfying this prerequisite, Numerical Methods and Optimization: An Introduction combines the materials from introductory numerical methods and introductory optimization courses into a single text. This classroom-tested approach enriches a standard numerical methods syllabus with optional chapters on numerical optimization and provides a valuable numerical methods background for students taking an introductory OR or optimization course. The first part of the text introduces the necessary mathematical background, the digital representation of numbers, and different types of errors associated with numerical methods. The second part explains how to solve typical problems using numerical methods. Focusing on optimization methods, the final part presents basic theory and algorithms for linear and nonlinear optimization. The book assumes minimal prior knowledge of the topics. Taking a rigorous yet accessible approach to the material, it includes some mathematical proofs as samples of rigorous analysis but in most cases, uses only examples to illustrate the concepts. While the authors provide a MATLAB® guide and code available for download, the book can be used with other software packages.

Author : Frank Neumann,Carsten Witt
Publisher : Springer Science & Business Media
Page : 216 pages
File Size : 55,8 Mb
Release : 2010-11-04
Category : Mathematics
ISBN : 9783642165443

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Bioinspired Computation in Combinatorial Optimization by Frank Neumann,Carsten Witt Pdf

Bioinspired computation methods such as evolutionary algorithms and ant colony optimization are being applied successfully to complex engineering problems and to problems from combinatorial optimization, and with this comes the requirement to more fully understand the computational complexity of these search heuristics. This is the first textbook covering the most important results achieved in this area. The authors study the computational complexity of bioinspired computation and show how runtime behavior can be analyzed in a rigorous way using some of the best-known combinatorial optimization problems -- minimum spanning trees, shortest paths, maximum matching, covering and scheduling problems. A feature of the book is the separate treatment of single- and multiobjective problems, the latter a domain where the development of the underlying theory seems to be lagging practical successes. This book will be very valuable for teaching courses on bioinspired computation and combinatorial optimization. Researchers will also benefit as the presentation of the theory covers the most important developments in the field over the last 10 years. Finally, with a focus on well-studied combinatorial optimization problems rather than toy problems, the book will also be very valuable for practitioners in this field.

Author : Sébastien Bubeck
Publisher : Foundations and Trends (R) in Machine Learning
Page : 142 pages
File Size : 54,7 Mb
Release : 2015-11-12
Category : Convex domains
ISBN : 1601988605

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Convex Optimization by Sébastien Bubeck Pdf

This monograph presents the main complexity theorems in convex optimization and their corresponding algorithms. It begins with the fundamental theory of black-box optimization and proceeds to guide the reader through recent advances in structural optimization and stochastic optimization. The presentation of black-box optimization, strongly influenced by the seminal book by Nesterov, includes the analysis of cutting plane methods, as well as (accelerated) gradient descent schemes. Special attention is also given to non-Euclidean settings (relevant algorithms include Frank-Wolfe, mirror descent, and dual averaging), and discussing their relevance in machine learning. The text provides a gentle introduction to structural optimization with FISTA (to optimize a sum of a smooth and a simple non-smooth term), saddle-point mirror prox (Nemirovski's alternative to Nesterov's smoothing), and a concise description of interior point methods. In stochastic optimization it discusses stochastic gradient descent, mini-batches, random coordinate descent, and sublinear algorithms. It also briefly touches upon convex relaxation of combinatorial problems and the use of randomness to round solutions, as well as random walks based methods.

Author : Klaus Jansen,Samir Khuller
Publisher : Springer
Page : 282 pages
File Size : 53,5 Mb
Release : 2003-07-31
Category : Computers
ISBN : 9783540444367

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Approximation Algorithms for Combinatorial Optimization by Klaus Jansen,Samir Khuller Pdf

This book constitutes the refereed proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2000, held in Saarbrcken, Germany in September 2000. The 22 revised full papers presented together with four invited contributions were carefully reviewed and selected from 68 submissions. The topics dealt with include design and analysis of approximation algorithms, inapproximibility results, on-line problems, randomization techniques, average-case analysis, approximation classes, scheduling problems, routing and flow problems, coloring and partitioning, cuts and connectivity, packing and covering, geometric problems, network design, and various applications.

Author : I︠U︡riĭ Gavrilovich Evtushenko
Publisher : Unknown
Page : 584 pages
File Size : 53,7 Mb
Release : 1985
Category : Mathematical optimization
ISBN : UOM:39015009833701

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Numerical Optimization Techniques by I︠U︡riĭ Gavrilovich Evtushenko Pdf

Author : Andreas Öchsner,Resam Makvandi
Publisher : Springer Nature
Page : 232 pages
File Size : 48,9 Mb
Release : 2020-04-08
Category : Science
ISBN : 9783030433888

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Numerical Engineering Optimization by Andreas Öchsner,Resam Makvandi Pdf

This study aid on numerical optimization techniques is intended for university undergraduate and postgraduate mechanical engineering students. Optimization procedures are becoming more and more important for lightweight design, where weight reduction can, for example in the case of automotive or aerospace industry, lead to lower fuel consumption and a corresponding reduction in operational costs as well as beneficial effects on the environment. Based on the free computer algebra system Maxima, the authors present procedures for numerically solving problems in engineering mathematics as well as applications taken from traditional courses on the strength of materials. The mechanical theories focus on the typical one-dimensional structural elements, i.e., springs, bars, and Euler–Bernoulli beams, in order to reduce the complexity of the numerical framework and limit the resulting design to a low number of variables. The use of a computer algebra system and the incorporated functions, e.g., for derivatives or equation solving, allows a greater focus on the methodology of the optimization methods and not on standard procedures. The book also provides numerous examples, including some that can be solved using a graphical approach to help readers gain a better understanding of the computer implementation.