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SIAM Review / Volume 44 / Issue 4

SIAM Rev. 44, pp. 525-597 (73 pages)

Interior Methods for Nonlinear Optimization

Anders Forsgren, Philip E. Gill, and Margaret H. Wright

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Interior methods are an omnipresent, conspicuous feature of the constrained optimization landscape today, but it was not always so. Primarily in the form of barrier methods, interior-point techniques were popular during the 1960s for solving nonlinearly constrained problems. However, their use for linear programming was not even contemplated because of the total dominance of the simplex method. Vague but continuing anxiety about barrier methods eventually led to their abandonment in favor of newly emerging, apparently more efficient alternatives such as augmented Lagrangian and sequential quadratic programming methods. By the early 1980s, barrier methods were almost without exception regarded as a closed chapter in the history of optimization.
This picture changed dramatically with Karmarkar's widely publicized announcement in 1984 of a fast polynomial-time interior method for linear programming; in 1985, a formal connection was established between his method and classical barrier methods. Since then, interior methods have advanced so far, so fast, that their influence has transformed both the theory and practice of constrained optimization. This article provides a condensed, selective look at classical material and recent research about interior methods for nonlinearly constrained optimization.

© 2002 Society for Industrial and Applied Mathematics

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KEYWORDS

AMS Subject Headings

49J20, 49J15, 49M37, 49D37, 65F05, 65K05, 90C30

PUBLICATION DATA

ISSN

0036-1445 (print)  
1095-7200 (online)

Publisher

$abstract.society.value is a Member of CrossRef Society for Industrial and Applied Mathematics

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1137/S0036144502414942

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