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Algorithmic Principles of Mathematical Programming

  • Book
  • © 2002

Overview

Authors:
  1. Ulrich Faigle

    1. University of Cologne, Cologne, Germany

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  2. Walter Kern

    1. University of Twente, Enschede, The Netherlands

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    You can also search for this author in PubMed   Google Scholar

  3. Georg Still

    1. University of Twente, Enschede, The Netherlands

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Part of the book series: Texts in the Mathematical Sciences (TMS, volume 24)

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-x
    Download chapter PDF

  2. Real Vector Spaces

    • Ulrich Faigle, Walter Kern, Georg Still
    Pages 1-20

  3. Linear Equations and Linear Inequalities

    • Ulrich Faigle, Walter Kern, Georg Still
    Pages 21-53

  4. Polyhedra

    • Ulrich Faigle, Walter Kern, Georg Still
    Pages 55-70

  5. Linear Programs and the Simplex Method

    • Ulrich Faigle, Walter Kern, Georg Still
    Pages 71-94

  6. Lagrangian Duality

    • Ulrich Faigle, Walter Kern, Georg Still
    Pages 95-108

  7. An Interior Point Algorithm for Linear Programs

    • Ulrich Faigle, Walter Kern, Georg Still
    Pages 109-121

  8. Network Flows

    • Ulrich Faigle, Walter Kern, Georg Still
    Pages 123-151

  9. Complexity

    • Ulrich Faigle, Walter Kern, Georg Still
    Pages 153-172

  10. Integer Programming

    • Ulrich Faigle, Walter Kern, Georg Still
    Pages 173-196

  11. Convex Sets and Convex Functions

    • Ulrich Faigle, Walter Kern, Georg Still
    Pages 197-240

  12. Unconstrained Optimization

    • Ulrich Faigle, Walter Kern, Georg Still
    Pages 241-271

  13. Constrained Nonlinear Optimization

    • Ulrich Faigle, Walter Kern, Georg Still
    Pages 273-323

  14. Back Matter

    Pages 325-339
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Keywords

About this book

Algorithmic Principles of Mathematical Programming investigates the mathematical structures and principles underlying the design of efficient algorithms for optimization problems. Recent advances in algorithmic theory have shown that the traditionally separate areas of discrete optimization, linear programming, and nonlinear optimization are closely linked. This book offers a comprehensive introduction to the whole subject and leads the reader to the frontiers of current research. The prerequisites to use the book are very elementary. All the tools from numerical linear algebra and calculus are fully reviewed and developed. Rather than attempting to be encyclopedic, the book illustrates the important basic techniques with typical problems. The focus is on efficient algorithms with respect to practical usefulness. Algorithmic complexity theory is presented with the goal of helping the reader understand the concepts without having to become a theoretical specialist. Further theory is outlined and supplemented with pointers to the relevant literature.

Authors and Affiliations

  • University of Cologne, Cologne, Germany

    Ulrich Faigle

  • University of Twente, Enschede, The Netherlands

    Walter Kern, Georg Still

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