Computer Solution of Linear Programs

"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 numericalanalysts." --Mathematical Reviews

• 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.