Nonconvex Optimization and Its Applications

By: R. Horst, Panos M. Pardalos, Nguyen Van Thoai

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Paperback | 30 June 1995

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336 Pages

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Global optimization concerns the computation and characterization of global optima of nonlinear functions. Such problems are widespread in the mathematical modelling of real systems in a very wide range of applications and the last 30 years have seen the development of many new theoretical, algorithmic and computational contributions which have helped to solve globally multiextreme problems in important practical applications.
Most of the existing books on optimization focus on the problem of computing locally optimal solutions. Introduction to Global Optimization, however, is a comprehensive textbook on constrained global optimization that covers the fundamentals of the subject, presenting much new material, including algorithms, applications and complexity results for quadratic programming, concave minimization, DC and Lipschitz problems, and nonlinear network flow. Each chapter contains illustrative examples and ends with carefully selected exercises, designed to help students grasp the material and enhance their knowledge of the methods involved.
Audience: Students of mathematical programming, and all scientists, from whatever discipline, who need global optimization methods in such diverse areas as economic modelling, fixed charges, finance, networks and transportation, databases, chip design, image processing, nuclear and mechanical design, chemical engineering design and control, molecular biology, and environmental engineering.

Industry Reviews

`Each chapter contains illustrative examples and exercises. This excellent book is the first textbook on deterministic global optimization.'
Mathematical Reviews, 96g:90001
`The authors provide a nice selection of homework exercises (with solutions) at an appropriate level and a good mixture of theory, application, and numerical problems throughout the text. The text would be perfect for a course on global optimization.'
Interfaces, 28 (1998)
`Overall, this book provides an excellent introduction to the fascinating field of global optimization. The authors have used their extensive knowledge of and perspective on the field to create a coherent text that is accessible to a large audience that includes both students of mathematical programming and scientists who utilize optimization in their work.'
Journal of Global Optimization, 9 (1996)

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Non-Fiction Mathematics Optimisation Linear Programming Politics & Government Computing & I.T.Computer Programming & Software Development Applied Mathematics

Preface to the Second Edition
Preface to the First Edition
Fundamental Results	p. 1
Convex Sets and Functions	p. 1
General Properties of Optimization Problems	p. 10
Convex Envelops	p. 16
Kuhn-Tucker Conditions	p. 20
Second Order Optimality Conditions	p. 25
Duality in Nonlinear Programming	p. 26
Complexity Issues	p. 32
Quadratic Programming	p. 49
Quadratic Integer Programming	p. 51
Linear Complementarity Problem	p. 71
Complexity of Quadratic Optimization	p. 74
Enumerative Methods	p. 83
Separation and Interpolation	p. 86
General Concave Minimization	p. 109
Applications	p. 110
Basic Operations	p. 118
Cutting Plane Algorithms	p. 135
Outer Approximation Algorithms	p. 147
Inner Approximation	p. 157
Branch and Bound Algorithms	p. 162
A Simplicial Branch and Bound Approach	p. 182
D.C. Programming	p. 195
The Space of D.C. Functions	p. 196
Some Additional Applications	p. 201
Optimality Conditions	p. 206
The Canonical D.C. Program	p. 210
A Simplicial Branch and Bound Algorithm	p. 219
A Prismatic Algorithm	p. 224
Lipschitz Optimization	p. 237
Lipschitz Functions	p. 237
Lipschitz Optimization Problems	p. 240
Lower Bounds	p. 243
Branch and Bound Algorithms	p. 247
Implementation	p. 259
Global Optimization on Networks	p. 267
Some MCCFP Models and its Complexity	p. 270
Solution Methods	p. 276
Decomposition Algorithms	p. 291
Variable Decomposition: Conical Algorithm	p. 293
Variable Decomposition: Outer Approximation	p. 301
Constraint Decomposition: Conical Algorithm	p. 305
Constraint Decomposition: Cutting Algorithm	p. 311
Solutions	p. 317
Selected References	p. 341
Index	p. 349
Table of Contents provided by Blackwell. All Rights Reserved.

Nonconvex Optimization and Its Applications

At a Glance

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Industry Reviews

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