Computer Solution of Linear Programmes

Computer Solution of Linear Programmes

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Description

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. Numerical analysts, operations researchers, control theorists, applied mathematicians.show more

Product details

  • Hardback | 244 pages
  • 162.56 x 236.22 x 20.32mm | 430.91g
  • Oxford University Press Inc
  • New York, United States
  • English
  • 26 figures, 9 tables, bibliography
  • 0195042786
  • 9780195042788

Table of contents

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.show more