High Performance Optimization

By: Hans Frenk (Editor), Kees Roos (Editor), Tamas Terlaky (Editor)

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Hardcover | 1 November 1999

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504 Pages

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For a long time the techniques of solving linear optimization (LP) problems improved only marginally. Fifteen years ago, however, a revolutionary discovery changed everything. A new `golden age' for optimization started, which is continuing up to the current time. What is the cause of the excitement? Techniques of linear programming formed previously an isolated body of knowledge. Then suddenly a tunnel was built linking it with a rich and promising land, part of which was already cultivated, part of which was completely unexplored. These revolutionary new techniques are now applied to solve conic linear problems. This makes it possible to model and solve large classes of essentially nonlinear optimization problems as efficiently as LP problems. This volume gives an overview of the latest developments of such `High Performance Optimization Techniques'. The first part is a thorough treatment of interior point methods for semidefinite programming problems. The second part reviews today's most exciting research topics and results in the area of convex optimization.
Audience: This volume is for graduate students and researchers who are interested in modern optimization techniques.

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Non-Fiction Mathematics Optimisation Game Theory Applied Mathematics Number Theory Linear Programming Calculus & Mathematical Analysis Reference, Information & Interdisciplinary Subjects Research & Information Information theory Cybernetics & Systems Theory

List of Figures
List of Tables
Preface
Contributing Authors
Theory and Algorithms of Semidefinite Programming
Introduction	p. 3
Duality	p. 21
Polynomiality of Path-following Methods	p. 61
Self-Dual Embedding Technique	p. 93
Properties of the Central Path	p. 129
Superlinear Convergence	p. 143
Central Region Method	p. 157
Linear, Quadratic, Semidefinite Programming and Beyond
An Implementation of the Homogeneous Algorithm	p. 197
A Simplified Correctness Proof for Interior Point Algorithm	p. 233
New Analysis of Newton Methods for LCP	p. 245
Numerical Evaluation of SDPA	p. 267
Robust Modeling of Multi-Stage Portfolio Problems	p. 303
An Interior Point SQP Parallel BandB Method	p. 329
Solving Linear Ordering Problems	p. 349
Finite Element Methods for Solving Parabolic Inverse Problems	p. 367
Error Bounds For Quadratic Systems	p. 383
Squared Functional Systems and Optimization Problems	p. 405
Interior Point Methods: Current Status and Future Directions	p. 441
Index	p. 467
Table of Contents provided by Blackwell. All Rights Reserved.

High Performance Optimization

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Hardcover

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