Linear Programming: Mathematics, Theory and Algorithms - M. J. Panik

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Résumé :
Linear Programming provides an in-depth look at simplex based as well as the more recent interior point techniques for solving linear programming problems. Starting with a review of the mathematical underpinnings of these approaches, the text provides details of the primal and dual simplex methods with the primal-dual, composite, and steepest edge simplex algorithms. This then is followed by a discussion of interior point techniques, including projective and affine potential reduction, primal and dual affine scaling, and path following algorithms. Also covered is the theory and solution of the linear complementarity problem using both the complementary pivot algorithm and interior point routines. A feature of the book is its early and extensive development and use of duality theory. Audience: The book is written for students in the areas of mathematics, economics, engineering and management science, and professionals who need a sound foundation in the important and dynamic discipline of linear programming.

Sommaire:
1. Introduction and Overview. 2. Preliminary Mathematics. 3. Introduction to Linear Programming. 4. Duality Theory. 5. The Theory of Linear Programming. 6. Duality Theory Revisited. 7. Computational Aspects of Linear Programming. 8. One-Phase, Two-Phase, and Composite Methods of Linear Programming. 9. Computational Aspects of Linear Programming: Selected Transformations. 10. The Dual Simplex, Primal-Dual, and Complementary Pivot Methods. 11. Postoptimality Analysis I. 12. Postoptimality Analysis II. 13. Interior Point Methods. 14. Interior Point Algorithms for Solving Linear Complementary Problems. Appendix A: Updating the Basis Inverse. Appendix B: Steepest Edge Simplex Methods. Appendix C: Derivation of the Projection Matrix. References. Notation Index. Index.