线性和非线性规划（第3版）英文版 Liear ad Noliear Programmig 运筹学专业高年级本科生 研究生和工程人员参考用书 pdf kindle caj 下载 azw3 umd 电子版 夸克云

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Chapter 1.Introduction

1.1.Optimization

1.2.Types of Problems

1.3.Size of Problems

1.4.I***tive Algorithms and Convergence

PART Ⅰ Linear Programming

Chapter 2.Basic Properties of Linear Programs

2.1.Introduction

2.2.Examples of Linear Programming Problems

2.3.Basic Soluti***

2.4.The Fundamental Theorem of Linear Programming

2.5.Relati*** to Convexity

2.6.Exercises

Chapter 3.The Simplex Method

3.1.Pivots

3.2.Adjacent Extreme Points

3.3.Determining a Minimum Feasible Solution

3.4.Computational Procedure—Simplex Method

3.5.Artificial Variables

3.6.Matrix Form of the Simplex Method

3.7.The Revised Simplex Method

3.8.The Simplex Method and LU Decomposition

3.9.Decomposition

3.10.Summary

3.11.Exercises

Chapter 4.Duality

4.1.Dual Linear Programs

4.2.The Duality Theorem

4.3.Relati*** to the Simplex Procedure

4.4.Sensitivity and Complementary Slackness

4.5.The Dual Simplex Method

4.6.The—Primal—Dual Algorithm

4.7.Reduction of Linear Inequalities

4.8.Exercises

Chapter 5.Interior—Point Methods

5.1.Elements of Complexity Theory

5.2.The Simplex Method is not Polynomial—Time

5.3.The Ellipsoid Method

5.4.The Analytic Center

5.5.The Central Path

5.6.Solution Strategies

5.7.Termination and Initialization

5.8.Summary

5.9.Exercises

Chapter 6.Transportation and Network Flow Problems

6.1.The Transportation Problem

6.2.Finding a Basic Feasible Solution

6.3.Basis Triangularity

***.Simplex Method for Transportation Problems

6.5.The Assignment Problem

6.6.Basic Network Concepts

6.7.Minimum Cost Flow

6.8.Maximal Flow

6.9.Summary

6.10.Exercises

PART Ⅱ Unc***trained Problems

Chapter 7.Basic Properties of Soluti*** and Algorithms

7.1.First—Order Necessary Conditi***

7.2.Examples of Unc***trained Problems

7.3.Second—Order Conditi***

7.4.Convex and Concave Functi***

7.5.Minimization and Maximization of Convex Functi***

7.6.Zero—Order Conditi***

7.7.Global Convergence of Descent Algorithms

7.8.Speed of Convergence

7.9.Summary

7.10.Exercises

Chapter 8.Basic Descent Methods

8.1.Fibonacci and Golden Section Search

8.2.Line Search by Curve Fitting

8.3.Global Convergence of Curve Fitting

8.4.Closedness of Line Search Algorithms

8.5.Inaccurate Line Search

8.6.The Method of Steepest Descent

8.7.Applicati*** of the Theory

8.8.Newton's Method

8.9.Coordinate Descent Methods

8.10.Spacer Steps

8.11.Summary

8.12.Exercises

Chapter 9.Conjugate Direction Methods

9.1.Conjugate Directi***

9.2.Descent Properties of the Conjugate Direction Method

9.3.The Conjugate Gradient Method

9.4.The C—***ethod as an Optimal Process

9.5.The Partial Conjugate Gradient Method

9.6.Extension to Nonquadratic Problems

9.7.Parallel Tangents

9.8.Exercises

Chapter 10.Quasi—Newton Methods

10.1.Modified Newton Method

10.2.C***truction of the Inverse

10.3.Davidon—Fletcher—Powell Method

10.4.The Broyden Family

10.5.Convergence Properties

10.6.Scaling

10.7.Memoryless Quasi—Newton Methods

10.8.Combination of Steepest Descent and Newton's Method

10.9.Summary

10.10.Exercises

PART Ⅲ C***trained Minimization

Chapter 11.C***trained Minimization Conditi***

1.1.C***traints

1.2.Tangent Plane

1.3.First—Order Necessary Conditi***（Equality C***traints）

1.4.Examples

1.5.Second—Order Conditi***

1.6.Eigenvalues in Tangent Subspace

1.7.Sensitivity

1.8.Inequality C***traints

1.9.Zero—Order Conditi*** and Lagrange Multipliers

1.10.Summary

1.11.Exercises

Chapter 12.Primal Methods

12.1.Advantage of Primal Methods

12.2.Feasible Direction Methods

12.3.Active Set Methods

12.4.The Gradient Projection Method

12.5.Convergence Rate of the Gradient Projection Method

12.6.The Reduced Gradient Method

12.7.Convergence Rate of the Reduced Gradient Method

12.8.Variati***

12.9.Summary

12.10.Exercises

Chapter 13.Penalty and Barrier Methods

13.1.Penalty Methods

13.2.Barrier Methods

13.3.Properties of Penalty and Barrier Functi***

13.4.Newton's Method and Penalty Functi***

13.5.Conjugate Gradients and Penalty Methods

13.6.Normalization of Penalty Functi***

13.7.Penalty Functi*** and Gradient Projection

13.8.Exact Penalty Functi***

13.9.Summary

13.10.Exercises

Chapter 14.Dual and Cutting Plane Methods

14.1.Global Duality

14.2.Local Duality

14.3.Dual Canonical Convergence Rate

14.4.Separable Problems

14.5.Augmented Lagrangians

14.6.The Dual Viewpoint

14.7.Cutting Plane Methods

14.8.Kelley's Convex Cutting Plane Algorithm

14.9.Modificati***

14.10.Exercises

Chapter 15.Primal—Dual Methods

15.1.The Standard Problem

15.2.Strategies

15.3.A Simple Merit Function

15.4.Basic Primal—Dual Methods

15.5.Modified Newton Methods

15.6.Descent Properties

15.7.Rate of Convergence

15.8.Interior Point Methods

15.9.Semidefinite Programming

15.10.Summary

15.11.Exercises

Appendix A.Mathematical Review

A.1.Sets

A.2.Matrix Notation

A.3.Spaces

A.4.Eigenvalues and Quadratic Forms

A.5.Topological Concepts

A.6.Functi***

Appendix B.Convex Sets

B.1.Basic Definiti***

B.2.Hyperplanes and Polytopes

B.3.Separating and Supporting Hyperplanes

B.4.Extreme Points

Appendix C.Gaussian Elimination

Bibliography

Index

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