Description
Book SynopsisThis 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.
Trade Review"Will provide a very solid background for anyone wanting to understand the ideas behind linear programming." --Choice "This book is distinguished from most other texts on linear programming by its detailed presentation of the ideas that underlie practical implementations of the simplex algorithm. It does not presume prior knowledge of the theory of linear programming or the simplex algorithm." --The American Mathematical Monthly "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 interesting topics not often encountered in competing literature. . . . Strongly recommended to anyone interested in linear programming including economists, engineers and numerical analysts." --Mathematical Reviews
Table of ContentsPART 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.
