Approximation and Complexity in Numerical Optimization

Author: Panos M. Pardalos
Publisher: Springer Science & Business Media
ISBN: 1475731450
Format: PDF, ePub
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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.

Discrete and Computational Geometry

Author: Boris Aronov
Publisher: Springer Science & Business Media
ISBN: 3642555667
Format: PDF, Kindle
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An impressive collection of original research papers in discrete and computational geometry, contributed by many leading researchers in these fields, as a tribute to Jacob E. Goodman and Richard Pollack, two of the ‘founding fathers’ of the area, on the occasion of their 2/3 x 100 birthdays. The topics covered by the 41 papers provide professionals and graduate students with a comprehensive presentation of the state of the art in most aspects of discrete and computational geometry, including geometric algorithms, study of arrangements, geometric graph theory, quantitative and algorithmic real algebraic geometry, with important connections to algebraic geometry, convexity, polyhedral combinatorics, the theory of packing, covering, and tiling. The book serves as an invaluable source of reference in this discipline.

Operations Research Proceedings 2003

Author: Dino Ahr
Publisher: Springer Science & Business Media
ISBN: 3642170226
Format: PDF, ePub, Mobi
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This volume contains a selection of papers referring to lectures presented at the symposium "Operations Research 2003" (OR03) held at the Ruprecht Karls-Universitiit Heidelberg, September 3 - 5, 2003. This international con ference took place under the auspices of the German Operations Research So ciety (GOR) and of Dr. Erwin Teufel, prime minister of Baden-Wurttemberg. The symposium had about 500 participants from countries all over the world. It attracted academians and practitioners working in various field of Opera tions Research and provided them with the most recent advances in Opera tions Research and related areas in Economics, Mathematics, and Computer Science. The program consisted of 4 plenary and 13 semi-plenary talks and more than 300 contributed papers selected by the program committee to be presented in 17 sections. Due to a limited number of pages available for the proceedings volume, the length of each article as well as the total number of accepted contributions had to be restricted. Submitted manuscripts have therefore been reviewed and 62 of them have been selected for publication. This refereeing procedure has been strongly supported by the section chairmen and we would like to express our gratitude to them. Finally, we also would like to thank Dr. Werner Muller from Springer-Verlag for his support in publishing this proceedings volume.

From Convexity to Nonconvexity

Author: R.P. Gilbert
Publisher: Springer
ISBN:
Format: PDF
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This collection of papers is dedicated to the memory of Gaetano Fichera, a great mathematician and also a good friend to the editors. Regrettably it took an unusual amount of time to bring this collection out. This was primarily due to the fact that the main editor who had collected all of the materials, for this volume, P. D. Panagiotopoulos, died unexpectedly during the period when we were editing the manuscript. The other two editors in appreciation of Panagiotopoulos' contribution to this field, believe it is therefore fitting that this collection be dedicated to his memory also. The theme of the collection is centered around the seminal research of G. Fichera on the Signorini problem. Variants on this idea enter in different ways. For example, by bringing in friction the problem is no longer self-adjoint and the minimization formulation is not valid. A large portion of this collection is devoted to survey papers concerning hemivariational methods, with a main point of its application to nonsmooth mechanics. Hemivariational inequali ties, which are a generalization of variational inequalities, were pioneered by Panagiotopoulos. There are many applications of this theory to the study of non convex energy functionals occurring in many branches of mechanics. An area of concentration concerns contact problems, in particular, quasistatic and dynamic contact problems with friction and damage. Nonsmooth optimization methods which may be divided into the main groups of subgradient methods and bundle methods are also discussed in this collection.

Complexity in Numerical Optimization

Author: P M Pardalos
Publisher: World Scientific
ISBN: 9814504084
Format: PDF, ePub, Docs
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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. Contents:Average Performance of a Self-Dual Interior Point Algorithm for Linear Programming (K M Anstreicher et al.)The Complexity of Approximating a Nonlinear Program (M Bellare & P Rogaway)Algorithms for the Least Distance Problem (P Berman et al.)Translational Cuts for Convex Minimization (J V Burke et al.)Maximizing Concave Functions in Fixed Dimension (E Cohen & N Megiddo)The Complexity of Allocating Resources in Parallel: Upper and Lower Bounds (E J Friedman)Complexity Issues in Nonconvex Network Flow Problems (G M Guisewite & P M Pardalos)A Classification of Static Scheduling Problems (J W Herrmann et al.)Complexity of Single Machine Hierarchical Scheduling: A Survey (C-Y Lee & G Vairaktarakis)Performance Driven Graph Enchancement Problems (D Paik & S Sahni)Parametric Flows, Weighted Means of Cuts, and Fractional Combinatorial Optimization (T Radzik)Some Complexity Issues Involved in the Construction of Test Cases for NP-Hard Problems (L A Sanchis)Maximizing Nonlinear Concave Functions in Fixed Dimension (S Toledo)A Note on the Complexity of Fixed-Point Computation for Noncontractive Maps (C W Tsay & K Sikorski)Polynomial Time Weak Approximation Algorithms for Quadratic Programming (S A Vavasis)Complexity Results for a Class of Min-Max Problems with Robust Optimization Applications (G Yu & P Kouvelis)and other papers Readership: Applied mathematicians and computer scientists. keywords:

Lectures on Modern Convex Optimization

Author: Aharon Ben-Tal
Publisher: SIAM
ISBN: 0898714915
Format: PDF, Docs
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Here is a book devoted to well-structured and thus efficiently solvable convex optimization problems, with emphasis on conic quadratic and semidefinite programming. The authors present the basic theory underlying these problems as well as their numerous applications in engineering, including synthesis of filters, Lyapunov stability analysis, and structural design. The authors also discuss the complexity issues and provide an overview of the basic theory of state-of-the-art polynomial time interior point methods for linear, conic quadratic, and semidefinite programming. The book's focus on well-structured convex problems in conic form allows for unified theoretical and algorithmical treatment of a wide spectrum of important optimization problems arising in applications.

Books in Print

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Books in print is the major source of information on books currently published and in print in the United States. The database provides the record of forthcoming books, books in-print, and books out-of-print.

Minimax and Applications

Author: Ding-Zhu Du
Publisher: Springer Science & Business Media
ISBN: 1461335574
Format: PDF, ePub, Mobi
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Techniques and principles of minimax theory play a key role in many areas of research, including game theory, optimization, and computational complexity. In general, a minimax problem can be formulated as min max f(x, y) (1) ",EX !lEY where f(x, y) is a function defined on the product of X and Y spaces. There are two basic issues regarding minimax problems: The first issue concerns the establishment of sufficient and necessary conditions for equality minmaxf(x,y) = maxminf(x,y). (2) "'EX !lEY !lEY "'EX The classical minimax theorem of von Neumann is a result of this type. Duality theory in linear and convex quadratic programming interprets minimax theory in a different way. The second issue concerns the establishment of sufficient and necessary conditions for values of the variables x and y that achieve the global minimax function value f(x*, y*) = minmaxf(x, y). (3) "'EX !lEY There are two developments in minimax theory that we would like to mention.

Numerical Optimization

Author: Jorge Nocedal
Publisher: Springer Science & Business Media
ISBN: 0387400656
Format: PDF, Kindle
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Optimization is an important tool used in decision science and for the analysis of physical systems used in engineering. One can trace its roots to the Calculus of Variations and the work of Euler and Lagrange. This natural and reasonable approach to mathematical programming covers numerical methods for finite-dimensional optimization problems. It begins with very simple ideas progressing through more complicated concepts, concentrating on methods for both unconstrained and constrained optimization.