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High Performance Optimization

  • Book
  • © 2000

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Editors:
  1. Hans Frenk

    1. Erasmus University, Rotterdam, The Netherlands

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  2. Kees Roos

    1. Delft University of Technology, The Netherlands

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  3. Tamás Terlaky

    1. Delft University of Technology, The Netherlands

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  4. Shuzhong Zhang

    1. Erasmus University, Rotterdam, The Netherlands

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Part of the book series: Applied Optimization (APOP, volume 33)

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About this book

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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Table of contents (18 chapters)

  1. Front Matter

    Pages i-xxii
    Download chapter PDF

  2. Theory and Algorithms of Semidefinite Programming

    1. Front Matter

      Pages 1-1
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    2. Introduction

      • Hans Frenk, Kees Roos, Tamás Terlaky, Shuzhong Zhang
      Pages 3-20

    3. Duality

      • Hans Frenk, Kees Roos, Tamás Terlaky, Shuzhong Zhang
      Pages 21-60

    4. Polynomiality of Path-Following Methods

      • Hans Frenk, Kees Roos, Tamás Terlaky, Shuzhong Zhang
      Pages 61-91

    5. Self-Dual Embedding Technique

      • Hans Frenk, Kees Roos, Tamás Terlaky, Shuzhong Zhang
      Pages 93-127

    6. Properties of the Central Path

      • Hans Frenk, Kees Roos, Tamás Terlaky, Shuzhong Zhang
      Pages 129-141

    7. Superlinear Convergence

      • Hans Frenk, Kees Roos, Tamás Terlaky, Shuzhong Zhang
      Pages 143-155

    8. Central Region Method

      • Hans Frenk, Kees Roos, Tamás Terlaky, Shuzhong Zhang
      Pages 157-194

  3. Linear, Quadratic, Semidefinite Programming and Beyond

    1. Front Matter

      Pages 195-195
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    2. The Mosek Interior Point Optimizer for Linear Programming: An Implementation of the Homogeneous Algorithm

      • Erling D. Andersen, Knud D. Andersen
      Pages 197-232

    3. A Simplification to “A Primal-Dual Interior Point Method Whose Running Time Depends Only on the Constraint Matrix”

      • Stephen A. Vavasis, Yinyu Ye
      Pages 233-243

    4. New Complexity Analysis of Primal-Dual Newton Methods for P *(κ) Linear Complementarity Problems

      • Jiming Peng, Cornelis Roos, Tamás Terlaky
      Pages 245-265

    5. Numerical Evaluation of SDPA (Semidefinite Programming Algorithm)

      • Katsuki Fujisawa, Mituhiro Fukuda, Masakazu Kojima, Kazuhide Nakata
      Pages 267-301

    6. Robust Modeling of Multi-Stage Portfolio Problems

      • Aharon Ben-Tal, Tamar Margalit, Arkadi Nemirovski
      Pages 303-328

    7. Computational Experience of an Interior-Point SQP Algorithm in a Parallel Branch-and-Bound Framework

      • Eva K. Lee, John E. Mitchell
      Pages 329-347

    8. Solving Linear Ordering Problems with a Combined Interior Point/Simplex Cutting Plane Algorithm

      • John E. Mitchell, Brian Borchers
      Pages 349-366

    9. Finite Element Methods for Solving Parabolic Inverse Problems

      • Yee Lo Keung, Jun Zou
      Pages 367-381

    10. Error Bounds for Quadratic Systems

      • Zhi-Quan Luo, Jos F. Sturm
      Pages 383-404

    11. Squared Functional Systems and Optimization Problems

      • Yurii Nesterov
      Pages 405-440
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Editors and Affiliations

  • Erasmus University, Rotterdam, The Netherlands

    Hans Frenk, Shuzhong Zhang

  • Delft University of Technology, The Netherlands

    Kees Roos, Tamás Terlaky

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