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＜電子ブック＞
Interior Point Methods of Mathematical Programming / edited by Tamás Terlaky
(Applied Optimization ; 5)

版	1st ed. 1996.
出版者	(New York, NY : Springer US : Imprint: Springer)
出版年	1996
本文言語	英語
大きさ	XXII, 530 p : online resource
著者標目	Terlaky, Tamás editor SpringerLink (Online service)
件　名	LCSH:Mathematical optimization LCSH:Operations research LCSH:Management science LCSH:Electrical engineering FREE:Optimization FREE:Operations Research, Management Science FREE:Operations Research and Decision Theory FREE:Electrical and Electronic Engineering
一般注記	I Linear Programming -- 1 Introduction to the Theory of Interior Point Methods -- 2 Affine Scaling Algorithm -- 3 Target-Following Methods for Linear Programming -- 4 Potential Reduction Algorithms -- 5 Infeasible-Interior-Point Algorithms -- 6 Implementation of Interior-Point Methods for Large Scale Linear Programs -- II Convex Programming -- 7 Interior-Point Methods for Classes of Convex Programs -- 8 Complementarity Problems -- 9 Semidefinite Programming -- 10 Implementing Barrier Methods for Nonlinear Programming -- III Applications, Extensions -- 11 Interior point Methods for Combinatorial Optimization -- 12 Interior Point Methods for Global Optimization -- 13 Interior Point Approaches for the VLSI Placement Problem One has to make everything as simple as possible but, never more simple. Albert Einstein Discovery consists of seeing what every­ body has seen and thinking what nobody has thought. Albert S. ent_Gyorgy; The primary goal of this book is to provide an introduction to the theory of Interior Point Methods (IPMs) in Mathematical Programming. At the same time, we try to present a quick overview of the impact of extensions of IPMs on smooth nonlinear optimization and to demonstrate the potential of IPMs for solving difficult practical problems. The Simplex Method has dominated the theory and practice of mathematical pro­ gramming since 1947 when Dantzig discovered it. In the fifties and sixties several attempts were made to develop alternative solution methods. At that time the prin­ cipal base of interior point methods was also developed, for example in the work of Frisch (1955), Caroll (1961), Huard (1967), Fiacco and McCormick (1968) and Dikin (1967). In 1972 Klee and Minty made explicit that in the worst case some variants of the simplex method may require an exponential amount of work to solve Linear Programming (LP) problems. This was at the time when complexity theory became a topic of great interest. People started to classify mathematical programming prob­ lems as efficiently (in polynomial time) solvable and as difficult (NP-hard) problems. For a while it remained open whether LP was solvable in polynomial time or not. The break-through resolution ofthis problem was obtained by Khachijan (1989) HTTP:URL=https://doi.org/10.1007/978-1-4613-3449-1

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