عنوان

In-Depth Analysis of Linear Programming

(Number (ISBN

9048158516

(Number (ISBN

9401597596

(Number (ISBN

9789048158515

(Number (ISBN

9789401597593

Number

b592013

Title Proper

In-Depth Analysis of Linear Programming

General Material Designation

[Book]

First Statement of Responsibility

by F. P. Vasilyev, A. Yu. Ivanitskiy.

Place of Publication, Distribution, etc.

Dordrecht

Name of Publisher, Distributor, etc.

Springer Netherlands : Imprint: Springer

Date of Publication, Distribution, etc.

2001

Specific Material Designation and Extent of Item

(XIV, 312 p. :)

Text of Note

Bibliographic Level Mode of Issuance: Monograph.

Text of Note

1. Simplex Method --; 2. The Main Theorems of Linear Programming --; 3. Dual Simplex Method --; 4. Criterion of Stability --; 5. Regularization Methods --; 6. Polynomial Methods in Linear Programming --; Notation --; References.

Text of Note

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.

Computer science -- Mathematics.

Computers.

Mathematics.

Class number

Book number

by F. P. Vasilyev, A. Yu. Ivanitskiy.

A Yu Ivanitskiy

F P Vasilyev

Electronic name

[Book]

Y