Linear Programming Computation

With emphasis on computation, this book is a real breakthrough in the field of LP. In addition to conventional topics, such as the simplex method, duality, and interior-point methods, all deduced in a fresh and clear manner, it introduces the state of the art by highlighting brand-new and advanced results, including efficient pivot rules, Phase-I approaches, reduced simplex methods, deficient-basis methods, face methods, and pivotal interior-point methods. In particular, it covers the determination of the optimal solution set, feasible-point simplex method, decomposition principle for solving large-scale problems, controlled-branch method based on generalized reduced simplex framework for solving integer LP problems.

Introduction.- Geometry of the Feasible Region.- Simplex Method.- Duality principle and dual simplex method.- Implementation of the Simplex Method.- Sensitivity Analysis and Parametric LP.- Variants of the Simplex Method.- Decomposition Method.- Interior Point Method.- Integer Linear Programming (ILP).- Pivot Rule.- Dual Pivot Rule.- Simplex Phase-I Method.- Dual Simplex Phase-l Method.- Reduced Simplex Method.- Improved Reduced Simplex Method.- D-Reduced Simplex Method.- Criss-Cross Simplex Method.- Generalizing Reduced Simplex Method.- Deficient-Basis Method.- Dual Deficient-Basis Method.- Face Method.- Dual Face Method.- Pivotal interior-point Method.- Special Topics.- Appendix.- References.