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Field name	Details
Dewey Class	519.6
Title	Interior Point Methods of Mathematical Programming ([EBook] /) / edited by Tamás Terlaky.
Added Personal Name	Terlaky, Tamás editor.
Other name(s)	SpringerLink (Online service)
Publication	Boston, MA : : Springer US, , 1996.
Physical Details	XXII, 530 p. : online resource.
Series	Applied Optimization 1384-6485 ; ; 5
ISBN	9781461334491
Summary Note	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).:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-1-4613-3449-1
Links to Related Works	Subject References: Decision making . Electrical engineering . Management science . Mathematical optimization . Mathematics . Operation Research/Decision Theory . Operations research . Operations Research, Management Science . Optimization . Authors: Terlaky, Tamás . Corporate Authors: SpringerLink (Online service) . Series: Applied Optimization . Classification: 519.6 .

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Interior Point Methods of Mathematical Programming

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