Introduces the latest theory and applications in optimization, emphasizing constrained optimization. You'll find a host of practical business applications and non-business applications. The book offers free C programs to implement the major algorithms covered.
This Third Edition introduces the latest theory and applications in optimization. It emphasizes constrained optimization, beginning with linear programming and then proceeding to convex analysis, network flows, integer programming, quadratic programming, and convex optimization. You'll discover a host of practical business applications as well as non-business applications. With its focus on solving practical problems, the book features free C programs to implement the major algorithms covered. The book's accompanying website includes the C programs, JAVA tools, and new online instructional tools and exercises.
Basic Theory-The Simplex Method and Duality.- The Simplex Method.- Degeneracy.- Efficiency of the Simplex Method.- Duality Theory.- The Simplex Method in Matrix Notation.- Sensitivity and Parametric Analyses.- Implementation Issues.- Problems in General Form.- Convex Analysis.- Game Theory.- Regression.- Financial Applications.- Network-Type Problems.- Network Flow Problems.- Applications.- Structural Optimization.- Interior-Point Methods.- The Central Path.- A Path-Following Method.- The KKT System.- Implementation Issues.- The Affine-Scaling Method.- The Homogeneous Self-Dual Method.- Extensions.- Integer Programming.- Quadratic Programming.- Convex Programming.
From the reviews of the third edition:
"Robert Vanderbei's textbook on linear programming, now in its third edition, builds on many of the approaches used by Chvátal and includes up-to-date coverage of a number of topics, including interior point methods, that have become important in the 25 years since the publication of Chvátal's book. Vanderbei's book is divided into four parts. ... suitable for use in a first course in linear programming covering the simplex method at the advanced undergraduate or graduate level." (Brian Borchers, MathDL, May, 2008)
Preface.- Preface to 2nd edition.- Preface to 3rd edition.- Introduction.- The Simplex Method.- Degeneracy.- Efficiency of the Simplex Method.- Duality method.- The Simplex Method in matrix notation.- Sensitivity and parametric analyses.- Implementation issues.- Problems in general form.- Convex analysis.- Game theory.- Regression.- Financial applications.- Network flow problems.- Applications.- Structural optimization.- The central path.- A path-following method.- The KKT system.- Implementation issues.- The affine-scaling method.- The homogeneous self-dual method.- Integer programming.- Quadratic programming.- Convex programming.- Source listings.- Answers to selected exercises.- Bibliography.- Index.