Interior point approach to linear, quadratic and convex programming : algorithms and complexity

by D. den Hertog

This book describes the rapidly developing field of interior point methods (IPMs). An extensive analysis is given of path-following methods for linear programming, quadratic programming and convex programming. These methods, which form a subclass of interior point methods, follow the central path, which is an analytic curve defined by the problem. Relatively simple and elegant proofs for polynomiality are given. The theory is illustrated using several explicit examples. Moreover, an overview of other classes of IPMs is given. It is shown that all these methods rely on the same notion as the path-following methods: all these methods use the central path implicitly or explicitly as a reference path to go to the optimum. For specialists in IPMs as well as those seeking an introduction to IPMs. The book is accessible to any mathematician with basic mathematical programming knowledge.

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[目次]

  • Glossary of Symbols and Notations. 1. Introduction of IPMs. 2. The logarithmic barrier method. 3. The center method. 4. Reducing the complexity for LP. 5. Discussion of other IPMs. 6. Summary, conclusions and recommendations. Appendices: A. Self-concordance proofs. B. General technical lemmas. Bibliography. Index.

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この本の情報

書名 Interior point approach to linear, quadratic and convex programming : algorithms and complexity
著作者等 Hertog, D. den
Hertog D.Den
シリーズ名 Mathematics and its applications
出版元 Kluwer Academic Publishers
刊行年月 c1994
ページ数 xii, 208 p.
大きさ 25 cm
ISBN 0792327349
NCID BA22313794
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言語 英語
出版国 オランダ
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