Advances in Optimization and Linear Programming

✍ Scribed by Ivan Stanimirović

• Publisher: Apple Academic Press
• Year: 2022
• Tongue: English
• Leaves: 204
• Edition: 1
• Category: Library

✦ Synopsis

This new volume provides the information needed to understand the simplex method, the revised simplex method, dual simplex method, and more for solving linear programming problems.

Following a logical order, the book first gives a mathematical model of the linear problem programming and describes the usual assumptions under which the problem is solved. It gives a brief description of classic algorithms for solving linear programming problems as well as some theoretical results. It goes on to explain the definitions and solutions of linear programming problems, outlining the simplest geometric methods, and showing how they can be implemented. Practical examples are included along the way. The book concludes with a discussion of multi-criteria decision-making methods.

This volume is a highly useful guide to linear programming for professors and students in optimization and linear programming.

✦ Table of Contents

Cover
Half Title
Title Page
Copyright Page
About the Author
Table of Contents
Preface
1 Introduction
1.1 Multiobjective Optimization
1.2 Symbolic Transformations in Multi-Sector Optimization
1.3 Pareto Optimality Test
1.4 The Method of Weight Coefficients
1.5 Mathematical Model
1.6 Properties of a Set of Constraints
1.7 Geometrical Method
2 Simplex Method
2.1 Properties of Simplex Methods
2.2 The Algebraic Essence of the Simplex Method
2.3 The Term Tucker’s Tables and the Simplex Method for Basic Permissible Canonical Forms
2.4 Algorithm of Simplex Method
2.5 Determination of the Initial Basic Permissible Solution
2.6 Two-Phase Simplex Methods
2.6.1 A Two-Phase Simplex Method That Uses Artificial Variables
2.6.2 Two-Phase Simplex Method Without Artificial Variables
2.7 BigM Method
2.8 Duality in Linear Programming
2.9 Dual Simplex Method
2.10 Elimination of Equations and Free Variables
2.11 Revised Simplex Method
2.12 Cycling Concept and Anti-Cyclic Rules
2.13 Complexity of Simplex Methods and Minty-Klee Polyhedra
3 Three Direct Methods in Linear Programming
3.1 Basic Terms
3.2 Minimum Angle Method
3.3 Dependent Constraints and Application of Game Theory
3.4 Algorithms and Implementation Details
3.5 Direct Heuristic Algorithm with General Inverses
Bibliography
Index