Cover Image
Read Now

Linear Programming A Modern Integrated Analysis

In Linear Programming: A Modern Integrated Analysis, both boundary (simplex) and interior point methods are derived from the complementary slackness theorem and, unlike most books, the duality theorem is derived from Farkas's Lemma, which is proved as a convex separation theorem. The tedium of...

Full description

Bibliographic Details
Main Author: Saigal, Romesh
Format: eBook
Language:English
Published: New York, NY Springer US 1995, 1995
Edition:1st ed. 1995
Series:International Series in Operations Research & Management Science
Subjects:
Operations Research
Optimization
Calculus Of Variations And Optimization
Mathematical Modeling And Industrial Mathematics
Mathematical Optimization
Operations Research And Decision Theory
Calculus Of Variations
Mathematical Models
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 1 Introduction
  • 1.1 The Problem
  • 1.2 Prototype Problems
  • 1.3 About this Book
  • 1.4 Notes
  • 2 Background
  • 2.1 Real Analysis
  • 2.2 Linear Algebra and Matrix Analysis
  • 2.3 Numerical Linear Algebra
  • 2.4 Convexity and Separation Theorems
  • 2.5 Linear Equations and Inequalities
  • 2.6 Convex Polyhedral Sets
  • 2.7 Nonlinear System of Equations
  • 2.8 Notes
  • 3 Duality Theory and Optimality Conditions
  • 3.1 The Dual Problem
  • 3.2 Duality Theorems
  • 3.3 Optimality and Complementary Slackness
  • 3.4 Complementary Pair of Variables
  • 3.5 Degeneracy and Uniqueness
  • 3.6 Notes
  • 4 Boundary Methods
  • 4.1 Introduction
  • 4.2 Primal Simplex Method
  • 4.3 Bounded Variable Simplex Method
  • 4.4 Dual Simplex Method
  • 4.5 Primal — Dual Method
  • 4.6 Notes
  • 5 Interior Point Methods
  • 5.1 Primal Affine Scaling Method
  • 5.2 Degeneracy Resolution by Step-Size Control
  • 5.3 Accelerated Affine Scaling Method
  • 5.4 Primal Power Affine Scaling Method
  • 5.5 Obtaining an Initial Interior Point
  • 5.6 Bounded Variable Affine Scaling Method
  • 5.7 Affine Scaling and Unrestricted Variables
  • 5.8 Dual Affine Scaling Method
  • 5.9 Primal-Dual Affine Scaling Method
  • 5.10 Path Following or Homotopy Methods
  • 5.11 Projective Transformation Method
  • 5.12 Method and Unrestricted Variables
  • 5.13 Notes
  • 6 Implementation
  • 6.1 Implementation of Boundary Methods
  • 6.2 Implementation of Interior Point Methods
  • 6.3 Notes
  • A Tables

Similar Items