Ebook: Interior Point Techniques in Optimization: Complementarity, Sensitivity and Algorithms
Author: Benjamin Jansen (auth.)
- Tags: Optimization, Operation Research/Decision Theory, Theory of Computation, Statistics general
- Series: Applied Optimization 6
- Year: 1997
- Publisher: Springer US
- Edition: 1
- Language: English
- pdf
Operations research and mathematical programming would not be as advanced today without the many advances in interior point methods during the last decade. These methods can now solve very efficiently and robustly large scale linear, nonlinear and combinatorial optimization problems that arise in various practical applications. The main ideas underlying interior point methods have influenced virtually all areas of mathematical programming including: analyzing and solving linear and nonlinear programming problems, sensitivity analysis, complexity analysis, the analysis of Newton's method, decomposition methods, polynomial approximation for combinatorial problems etc. This book covers the implications of interior techniques for the entire field of mathematical programming, bringing together many results in a uniform and coherent way. For the topics mentioned above the book provides theoretical as well as computational results, explains the intuition behind the main ideas, gives examples as well as proofs, and contains an extensive up-to-date bibliography.
Audience: The book is intended for students, researchers and practitioners with a background in operations research, mathematics, mathematical programming, or statistics.
Content:
Front Matter....Pages i-xiv
Introduction....Pages 1-11
The Theory of Linear Programming....Pages 13-26
Sensitivity Analysis in Linear Programming....Pages 27-55
Sensitivity Analysis in Quadratic Programming....Pages 57-69
Primal-Dual Affine Scaling Methods for Linear Problems....Pages 71-99
Primal-Dual Affine Scaling Methods for Nonlinear Problems....Pages 101-128
Computational Results with Affine Scaling Methods....Pages 129-146
Target-Following for Linear Programming....Pages 147-194
Target-Following for Nonlinear Programming....Pages 195-219
Semidefinite Programming....Pages 221-239
Interior Point Methods in Decomposition....Pages 241-247
Back Matter....Pages 249-279
Content:
Front Matter....Pages i-xiv
Introduction....Pages 1-11
The Theory of Linear Programming....Pages 13-26
Sensitivity Analysis in Linear Programming....Pages 27-55
Sensitivity Analysis in Quadratic Programming....Pages 57-69
Primal-Dual Affine Scaling Methods for Linear Problems....Pages 71-99
Primal-Dual Affine Scaling Methods for Nonlinear Problems....Pages 101-128
Computational Results with Affine Scaling Methods....Pages 129-146
Target-Following for Linear Programming....Pages 147-194
Target-Following for Nonlinear Programming....Pages 195-219
Semidefinite Programming....Pages 221-239
Interior Point Methods in Decomposition....Pages 241-247
Back Matter....Pages 249-279
....