Linear Programming: Foundations and Extensions

Sampul Depan
Springer Science & Business Media, 29 Jun 2013 - 450 halaman

Linear Programming: Foundations and Extensions is an introduction to the field of optimization. The book emphasizes constrained optimization, beginning with a substantial treatment of linear programming, and proceeding to convex analysis, network flows, integer programming, quadratic programming, and convex optimization.

The book is carefully written. Specific examples and concrete algorithms precede more abstract topics. Topics are clearly developed with a large number of numerical examples worked out in detail.

Moreover, Linear Programming: Foundations and Extensions underscores the purpose of optimization: to solve practical problems on a computer. Accordingly, the book is coordinated with free efficient C programs that implement the major algorithms studied:

-The two-phase simplex method; -The primal-dual simplex method; -The path-following interior-point method; -The homogeneous self-dual methods.

In addition, there are online JAVA applets that illustrate various pivot rules and variants of the simplex method, both for linear programming and for network flows. These C programs and JAVA tools can be found on the book's webpage: . Also, check the book's webpage for new online instructional tools and exercises that have been added in the new edition.

 

Halaman terpilih

Isi

Introduction
4
The Simplex Method
13
Degeneracy
29
Efficiency of the Simplex Method
45
Duality Theory
55
The Simplex Method in Matrix Notation 89
88
Sensitivity and Parametric Analyses
111
Implementation Issues
125
Structural Optimization
259
The Central Path
277
A PathFollowing Method 291
290
The KKT System
307
Implementation Issues
315
The AffineScaling Method 333
332
The Homogeneous SelfDual Method
349
Integer Programming 373
372

Problems in General Form
151
Convex Analysis
161
Game Theory 173
172
Regression
189
Network Flow Problems 213
212
Applications
241
Quadratic Programming
395
Convex Programming 413
412
Appendix A Source Listings
425
Answers to Selected Exercises 433
432
Index
443
Hak Cipta

Edisi yang lain - Lihat semua

Linear Programming
Robert J. Vanderbei
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Linear Programming: Foundations and Extensions
Robert J Vanderbei
Pratinjau tidak tersedia - 2001

Istilah dan frasa umum

affine-scaling algorithm c¹x called central path chapter coefficients column complementarity compute constraints convex combinations corresponding defined denote diagonal matrix dual dictionary dual feasible dual problem dual simplex method dual slacks dual solution dual variables elimination entering arc entering variable example Exercise feasible solution formula given Hence inequality infeasible integer programming interior-point method leaving arc leaving variable linear complementarity problem linear programming problem matrix maximize minimize negative network flow problem node nonbasic variables nonlinear nonnegative nonzero notation objective function objective function value optimal solution path-following method permutation pivoting rules primal and dual primal dictionary primal feasible primal problem primal solution primal-dual quadratic programming right-hand side self-dual self-dual simplex method shown in Figure simplex method simply slack variables solve spanning tree step direction subject to Ax symmetric systems of equations tree solution upper bound vector w₁ write x₁ zero

Informasi bibliografi

JudulLinear Programming: Foundations and Extensions
Volume 37 dari International Series in Operations Research & Management Science
PengarangRobert J Vanderbei
Edisi2, berilustrasi
PenerbitSpringer Science & Business Media, 2013
ISBN1475756623, 9781475756623
Tebal450 halaman
  
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