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Theory and algorithms for linear optimization. An interior point approach. (English) Zbl 0954.65041
Chichester: Wiley. xxiv, 482 p. (1997).
This is the second edition of the highly successful book on the theory and algorithms for linear optimization. The book is not simply a collection of research papers. It is a comprehensive treatment of the area. It presents a unified framework for the interior point methods (IPMs), a new approach for solving linear programming problems grown out of N. Karmarkar’s seminal work [Combinatorica 4, 373-395 (1984; Zbl 0557.90065)]. Practically all aspects of IPMs are discussed including convergence, complexity, asymptotic behaviour and the key issues of implementation.
The four main parts of the book cover theory and complexity, the logarithmic barrier approach, the target following approach and miscellanous topics. The latter contains such valuable chapters like Karmarkar’s projective method, high-order methods and parametric and sensitivity analysis.
The book is mostly based on the research results of the authors but it includes all relevant material from other researchers. It is equally suitable for students and researchers interested in the area. The dependence graph of the chapters is a useful guide for readers at every level.

MSC:
65K05 Numerical mathematical programming methods
90C51 Interior-point methods
65-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to numerical analysis
90-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to operations research and mathematical programming
90C05 Linear programming
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