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بهینه سازی خطی پیشرفته 1

مطالبی را که در این درس مطالعه می کنیم به شرح زیر است.

CONTENTS

ONE: INTRODUCTION 1

1.1 The Linear Programming Problem

1.2 Linear Programming Modeling and Examples

1.3 Geometric Solution

1.4 The Requirement Space

TWO: LINEAR ALGEBRA, CONVEX ANALYSIS, AND

POLYHEDRAL SETS

2.1 Vectors

2.2 Matrices

2.3 Simultaneous Linear Equations

2.4 Convex Sets and Convex Functions

2.5 Polyhedral Sets and Polyhedral Cones

2.6 Extreme Points, Faces, Directions, and Extreme

Directions of Polyhedral Sets: Geometric Insights

2.7 Representation of Polyhedral Sets

THREE: THE SIMPLEX METHOD

3.1 Extreme Points and Optimality

3.2 Basic Feasible Solutions

3.3 Key to the Simplex Method

3.4 Geometric Motivation of the Simplex Method

3.5 Algebra of the Simplex Method

3.6 Termination: Optimality and Unboundedness

3.7 The Simplex Method

3.8 The Simplex Method in Tableau Format

FOUR: STARTING SOLUTION AND CONVERGENCE

4.1 The Initial Basic Feasible Solution

4.2 The Two-Phase Method

4.3 The Big-M Method

4.4 How Big Should Big-WBe?

4.5 The Single Artificial Variable Technique

4.6 Degeneracy, Cycling, and Stalling

4.7 Validation of Cycling Prevention Rules

FIVE: SPECIAL SIMPLEX IMPLEMENTATIONS AND

OPTIMALITY CONDITIONS

5.1 The Revised Simplex Method

5.2 The Simplex Method for Bounded Variables

5.3 Farkas' Lemma via the Simplex Method

5.4 The Karush-Kuhn-Tucker Optimality Conditions

SIX: DUALITY AND SENSITIVITY ANALYSIS

6.1 Formulation of the Dual Problem

6.2 Primal-Dual Relationships

6.3 Economic Interpretation of the Dual

6.4 The Dual Simplex Method

6.5 The Primal-Dual Method

6.6 Finding an Initial Dual Feasible Solution: The

Artificial Constraint Technique

6.7 Sensitivity Analysis

6.8 Parametric Analysis