Overview

For a long time the techniques of solving linear optimization (LP) problems improved only marginally. In the mid 1970s 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 developments in ""High Performance Optimization Techniques"". The first part is a treatment of interior point methods for semidefinite programming problems. The second part reviews research topics and results in the area of convex optimization.

Full Product Details

Author:   Hans Frenk ,  Kees Roos ,  Tamás Terlaky ,  Shuzhong Zhang
Publisher:   Springer
Imprint:   Springer
Edition:   1999 ed.
Volume:   33
Dimensions:   Width: 15.50cm , Height: 2.60cm , Length: 23.50cm
Weight:   0.916kg
ISBN:  

9780792360131

ISBN 10:   0792360133
Pages:   474
Publication Date:   30 November 1999
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Out of stock  
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Table of Contents

1 Introduction.- 2 Duality.- 3 Polynomiality of Path-following Methods.- 4 Self-Dual Embedding Technique.- 5 Properties of the Central Path.- 6 Superlinear Convergence.- 7 Central Region Method.- 8 An Implementation of the Homogeneous Algorithm.- 9 A Simplified Correctness Proof for Interior Point Algorithm.- 10 New Analysis of Newton Methods for LCP.- 11 Numerical Evaluation of SDPA.- 12 Robust Modeling of Multi-Stage Portfolio Problems.- 13 An Interior Point SQP Parallel B&B Method.- 14 Solving Linear Ordering Problems.- 15 Finite Element Methods for Solving Parabolic Inverse Problems.- 16 Error Bounds For Quadratic Systems.- 17 Squared Functional Systems and Optimization Problems.- 18 Interior Point Methods: Current Status and Future Directions.

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