In-Depth Analysis of Linear Programming

✍ Scribed by F. P. Vasilyev, A. Yu. Ivanitskiy (auth.)

• Publisher: Springer Netherlands
• Year: 2001
• Tongue: English
• Leaves: 320
• Edition: 1
• Category: Library

✦ Synopsis

Along with the traditional material concerning linear programming (the simplex method, the theory of duality, the dual simplex method), In-Depth Analysis of Linear Programming contains new results of research carried out by the authors.
For the first time, the criteria of stability (in the geometrical and algebraic forms) of the general linear programming problem are formulated and proved. New regularization methods based on the idea of extension of an admissible set are proposed for solving unstable (ill-posed) linear programming problems. In contrast to the well-known regularization methods, in the methods proposed in this book the initial unstable problem is replaced by a new stable auxiliary problem. This is also a linear programming problem, which can be solved by standard finite methods. In addition, the authors indicate the conditions imposed on the parameters of the auxiliary problem which guarantee its stability, and this circumstance advantageously distinguishes the regularization methods proposed in this book from the existing methods. In these existing methods, the stability of the auxiliary problem is usually only presupposed but is not explicitly investigated.
In this book, the traditional material contained in the first three chapters is expounded in much simpler terms than in the majority of books on linear programming, which makes it accessible to beginners as well as those more familiar with the area.

✦ Table of Contents

Front Matter....Pages i-xiii
Simplex Method....Pages 1-77
The Main Theorems of Linear Programming....Pages 79-118
Dual Simplex Method....Pages 119-166
Criterion of Stability....Pages 167-202
Regularization Methods....Pages 203-228
Polynomial Methods in Linear Programming....Pages 229-293
Back Matter....Pages 295-312

✦ Subjects

Optimization; Computational Mathematics and Numerical Analysis; Economic Theory; Operations Research, Management Science; Theory of Computation