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Rescaled proximal methods for linearly constrained convex problems

Published online by Cambridge University Press:  11 October 2007

Paulo J.S. Silva  and
Carlos Humes Jr.
Paulo J.S. Silva
Affiliation:
Instituto de Matemática e Estatística, Universidade de São Paulo, Brazil; pjssilva@ime.usp.br, chumes@usp.br
Carlos Humes Jr.
Affiliation:
Instituto de Matemática e Estatística, Universidade de São Paulo, Brazil; pjssilva@ime.usp.br, chumes@usp.br
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Abstract

We present an inexact interior point proximal method to solve linearly constrained convex problems. In fact, we derive a primal-dual algorithm to solve the KKT conditions of the optimization problem using a modified version of the rescaled proximal method. We also present a pure primal method. The proposed proximal method has as distinctive feature the possibility of allowing inexact inner steps even for Linear Programming. This is achieved by using an error criterion that bounds the subgradient of the regularized function, instead of using ϵ-subgradients of the original objective function. Quadratic convergence for LP is also proved using a more stringent error criterion.

Keywords

Interior proximal methodsLinearly constrained convex problems
Type
Research Article
Information
RAIRO - Operations Research , Volume 41 , Issue 4 , October 2007 , pp. 367 - 380
Copyright
© EDP Sciences, ROADEF, SMAI, 2007

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