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Table of contents (6 chapters)
Keywords
About this book
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.
Authors and Affiliations
Bibliographic Information
Book Title: In-Depth Analysis of Linear Programming
Authors: F. P. Vasilyev, A. Yu. Ivanitskiy
DOI: https://doi.org/10.1007/978-94-015-9759-3
Publisher: Springer Dordrecht
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eBook Packages: Springer Book Archive
Copyright Information: Springer Science+Business Media Dordrecht 2001
Hardcover ISBN: 978-1-4020-0085-0Published: 31 October 2001
Softcover ISBN: 978-90-481-5851-5Published: 01 December 2010
eBook ISBN: 978-94-015-9759-3Published: 29 June 2013
Edition Number: 1
Number of Pages: XIV, 312
Topics: Optimization, Computational Mathematics and Numerical Analysis, Economic Theory/Quantitative Economics/Mathematical Methods, Operations Research, Management Science, Theory of Computation