Computer Solution of Linear Programs by J. L. Nazareth

Computer Solution of Linear Programs

byJ. L. Nazareth

Hardcover | April 30, 1999

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This self-contained book provides a systematic account of the main algorithms derived from the simplex method and the means by which they may be organized into effective procedures for solving practical linear programming problems on a computer. The book begins by characterizing the problemand the method used to solve it, going on to deal with the practicalities of the subject, emphasizing concerns of implementation. The final section of the book discusses the basic principles of optimization: duality, decomposition, and homotopy. In conjunction with the simplex method, they eachlead to other key algorithms of linear programming. The author's approach is distinguished by his detailed exploration of ideas and issues that center on the need to structure data suitably, and to organize calculations in an efficient and numerically stable manner. Unlike many liner programmingtexts, the author's overall perspective is grounded in nonlinear programming rather than combinatorics.

About The Author

J. L. Nazareth is at University of California, Berkeley.
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Details & Specs

Title:Computer Solution of Linear ProgramsFormat:HardcoverDimensions:254 pages, 9.21 × 6.14 × 0.03 inPublished:April 30, 1999Publisher:Oxford University Press

The following ISBNs are associated with this title:

ISBN - 10:0195042786

ISBN - 13:9780195042788

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Table of Contents

PART I: BASIC THEORY AND METHOD1. Linear Programs and Their Solution2. The Simplex MethodPART II: PRACTICAL ASPECTS3. Problem Setup4. The Basis Matrix--Fundamentals of Numerical Computation and Numerical Linear Algebra5. The Basis Matrix--Factorizing and Solving6. The Basis Matrix--Updating and Solving7. Selection Strategies--Choosing the Entering and Exiting Variables8. Selection Strategies--Finding an Initial Feasible Solution9. Practical Implementation10. Mathematical Programming Systems in PracticePART III: OPTIMIZATION PRINCIPLE + SIMPLEX METHOD = LP ALGORITHM11. The Duality Principle and the Simplex Method12. The Decomposition Principle and the Simplex Method13. The Homotopy Principle and the Simplex Method

Editorial Reviews

"Well written, clear and well organized. Hence the arguments are easy to follow. Among the many books on linear programming now on the market it is one of the very best. Not only does it describe the simplex algorithm and several important variants but it also deals with many interestingtopics not often encountered in competing literature. . . . Strongly recommended to anyone interested in linear programming including economists, engineers and numerical analysts." --Mathematical Reviews