Interior Point Techniques in Optimization

1. Front Matter

   Pages i-xiv

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2. Introduction

   • Benjamin Jansen

   Pages 1-11

3. The Theory of Linear Programming

   • Benjamin Jansen

   Pages 13-26

4. Sensitivity Analysis in Linear Programming

   • Benjamin Jansen

   Pages 27-55

5. Sensitivity Analysis in Quadratic Programming

   • Benjamin Jansen

   Pages 57-69

6. Primal-Dual Affine Scaling Methods for Linear Problems

   • Benjamin Jansen

   Pages 71-99

7. Primal-Dual Affine Scaling Methods for Nonlinear Problems

   • Benjamin Jansen

   Pages 101-128

8. Computational Results with Affine Scaling Methods

   • Benjamin Jansen

   Pages 129-146

9. Target-Following for Linear Programming

   • Benjamin Jansen

   Pages 147-194

10. Target-Following for Nonlinear Programming

    • Benjamin Jansen

    Pages 195-219

11. Semidefinite Programming

    • Benjamin Jansen

    Pages 221-239

12. Interior Point Methods in Decomposition

    • Benjamin Jansen

    Pages 241-247

13. Back Matter

    Pages 249-279

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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.

• Approximation
• Newton's method
• algorithms
• calculus
• combinatorial optimization
• complexity
• linear optimization
• nonlinear optimization
• operations research
• optimization
• quadratic programming
• statistics

• Centre for Quantitative Methods CQM B.V., Eindhoven, The Netherlands

  Benjamin Jansen

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