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Theory and Algorithms for Linear Optimization: An Interior Point Approach

Theory and Algorithms for Linear Optimization: An Interior Point Approach

C. Roos, T. Terlaky, J.-Ph. Vial

ISBN: 978-0-470-86593-4

Feb 1997

508 pages

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$124.99

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Description

Linear Optimization (LO) is a widely taught and used mathematical technique that can also be applied to areas of science, commerce and industry. Because of advances in computer technology and developments in the field of interior point methods (IPM), problems that could not be solved years ago (because of lengthy time requirements) can now be solved in minutes by way of IPM approach to both the theory of LO and algorithms for LO (design, convergence, complexity and asymptotic behavior). Numerous exercises are provided to aid in understanding the material.
Partial table of contents:

INTRODUCTION: THEORY AND COMPLEXITY.

Duality Theory for Linear Optimization.

A Polynomial Algorithm for the Skew-Symmetric Model.

Solving the Canonical Problem.

THE LOGARITHMIC BARRIER APPROACH.

The Dual Logarithmic Barrier Method.

Initialization.

THE TARGET-FOLLOWING APPROACH.

The Primal-Dual Newton Method.

Application to the Method of Centers.

MISCELLANEOUS TOPICS.

Karmarkar's Projective Method.

More Properties of the Central Path.

Partial Updating.

High-Order Methods.

Parametric and Sensitivity Analysis.

Implementing Interior Point Methods.

Appendices.

Bibliography.

Indexes.