Computer solution of linear programs
著者
書誌事項
Computer solution of linear programs
（Monographs on numerical analysis）
Oxford University Press, 1987
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注記
Bibliography: p. 221-224
Includes index
内容説明・目次
内容説明
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 problem and the method used to solve it, and goes 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 each lead to other key algorithms of linear programming. The author's approach is distinguished by his detailed exploration of ideas and issues that centre on the need to structure
data suitably, and to organize calculations in an efficient and numerically stable manner. Unlike many linear programming texts, the author's overall perspective is grounded in nonlinear programming rather than combinatorics.
目次
- PART I - BASIC THEORY AND METHOD: Linear programs and their solution
- The simplex method. PART II - PRACTICAL ASPECTS: Problem setup
- The basis matrix - fundamentals of numerical computation and numerical linear algebra
- The basis matrix - factorising and solving
- The basis matrix - updating and solving
- Selection strategies - choosing the entering and exiting variables
- Selection strategies - finding an initial feasible solution
- Practical implementation
- Mathematical programming systems in practice. PART III - OPTIMIZATION PRINCIPLE + SIMPLEX METHOD = LP ALGORITHM: The duality principle and the simplex method
- The decomposition principle and the simplex method
- The homotopy principle and the simplex method
- Bibliography
- Index.
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