Exploring Interior-Point Linear Programming
Algorithms and Software
This book provides practitioners as well as students of this general methodology with an easily accessible introduction to the new class of algorithms known as interior-point methods for linear programming.
Linear programming is widely used in industry to solve complex planning and resource allocation problems. This book provides practitioners as well as students of this general methodology with an easily accessible introduction to the new class of algorithms known as interior-point methods for linear programming. In addition to presenting the theoretical and algorithmic background necessary for dealing with specific interior-point linear programming algorithms, it offers a review of modeling linear programming problems, a review of the simplex algorithm that has been used to solve linear programming problems in the past, and a complete user's guide to the software that is included with the book.The interior-point technique is proving especially powerful for the solution of large-scale linear programming problems, with better performance bounds than the simplex algorithm. For example, the U.S. Military airlift command has solved their scheduling problem using interior-point algorithms much faster and with a longer planning horizon than was possible with the simplex algorithms, and Delta expects to save millions of dollars by using interior-point methods to schedule their air crews and planes.The software package is designed for use on IBM-PC microcomputers (and compatibles), a platform that provides an ideal environment for students of linear programming interested in exploring and studying these new algorithms.Contents: Preparations. Introduction. Modeling Linear Optimization Problems. The Simplex Algorithm. A First Look at an Interior Point Algorithm. Algorithms. The Primal Algorithm. The Dual Algorithm. The Primal-Dual Algorithm. Implementation Issues. Solutions. The Integrated Environment. Command Line Operations. Appendixes.