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Mathematical Programming: Theory and Methods

Mathematical

Programming

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Mathematical Programming: Theory and Methods by S. M. Sinha Pub. Date: February 2006

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Mathematical Programming:

Theory and Methods, by S. M. Sinha

• ISBN: 813120376X

• Publisher: Elsevier Science & Technology Books

• Pub. Date: February 2006

Preface

This book is a result of my teaching mathematical programming to graduate

students of the University of Delhi for over thirty years. In preparing this book,

a special care has been made to see that it is self-contained and that it is suitable

both as a text and as a reference.

The book is divided in three parts. In Part 1, some mathematical topics have

been reviewed to aid the reader in understanding the material discussed and to

equip him with the ability to pursue further study. In Part 2, linear programming

from its origin to the latest developments have been included and Part 3 deals

with non-linear and dynamic programming including some special topics of recent

developments. Several examples and exercises of varying difficulties have been

provided to enable the reader to have a clear understanding of the concepts and

methods discussed in the text.

I am indebted to Prof. George B. Dantzig, who first introduced me to

stochastic programming, way back in 1961, when it was emerging as an important

area of development. I am grateful to Prof. J. Medhi who originally suggested

me to write a book on Mathematical Programming and to Prof. Roger J.B. Wets

for his encouragement in taking up this project. Special thanks are due to my

colleagues Prof. K. Sen, Prof. Manju Agarwal and Prof. J.M. Gupta for their

various suggestions and help during the preparation of the manuscript. I am also

thankful to my many students, particularly Dr. C.K. Jaggi and Dr. G.C. Tuteja

for their numerous help. I am specially thankful to my son Dr. Amit K. Sinha

for his help and continuous insistence for completing the book.

Finally, I must thank Mr. Sanjay Banerjee, Managing Director, Elsevier, South

and South-East Asia, for getting the book published.

Deltfi S.M. Sinha

Table of Contents

• Preface, Page vii

• Chapter 1 - Introduction, Pages 1-9

• Part - 1: Mathematical Foundations

• Chapter 2 - Basic theory of sets and functions, Pages 13-25

• Chapter 3 - Vector spaces, Pages 26-37

• Chapter 4 - Matrices and determinants, Pages 38-49

• Chapter 5 - Linear transformations and rank, Pages 50-55

• Chapter 6 - Quadratic forms and Eigenvalue problems, Pages 56-62

• Chapter 7 - Systems of linear equations and linear inequalities, Pages 63-

• Chapter 8 - Convex sets and convex cones, Pages 76-93

• Chapter 9 - Convex and concave functions, Pages 94-114

• Chapter 10 - Linear programming problems, Pages 117-131

• Chapter 11 - Simplex method: Theory and computation, Pages 132-144

• Chapter 12 - Simplex method: Initial basic feasible solution, Pages 145-157

• Chapter 13 - Degeneracy in linear programming, Pages 158-164

• Chapter 14 - The revised simplex method, Pages 165-176

• Chapter 15 - Duality in Linear Programming, Pages 177-198

• Chapter 16 - Variants of the simplex method, Pages 199-221

• Chapter 17 - Post-optimization problems: Sensitivity analysis and

parametric programming, Pages 222-235

• Chapter 18 - Bounded variable problems, Pages 236-244

• Chapter 19 - Transportation problems, Pages 245-274

• Chapter 20 - Assignment problems, Pages 275-290

• Chapter 21 - The decomposition principle for linear programs, Pages 291-

302

• Chapter 22 - Polynomial time algorithms for linear programming, Pages

303-320

• Chapter 23 - Nonlinear programming, Pages 323-339

• Chapter 24 - Quadratic programming, Pages 340-365

• Chapter 25 - Methods of nonlinear programming, Pages 366-422

• Chapter 26 - Duality in nonlinear programming, Pages 423-430

• Chapter 27 - Stochastic programming, Pages 431-461

• Chapter 28 - Some special topics in mathematical programming, Pages

462-501

• Chapter 29 - Dynamic programming, Pages 502-533

• Bibliography, Pages 534-565

• Index, Pages 567-572

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sucker228

2017-04-15

清晰度还可以,扫描版转 OCR.有目录,总体还不错,值得下载,反正就1分.
猫咪的晴天

2014-07-24

很好的资源，完整清晰，有目录！
farrelly

2015-01-15

学习优化理论很好的入门教材

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