On the convergence of the entropy-exponential penalty trajectories and generalized proximal point methods in semidefinite optimization
type: Item
instance of: scholarly article
title: On the convergence of the entropy-exponential penalty trajectories and generalized proximal point methods in semidefinite optimization
zbMATH Open document ID: 1205.90216
author: R. C. M. Silva
author: O. P. Ferreira
author: P. R. Oliveira
published in: Journal of Global Optimization
publication date: 2009-11-16T00:00:00Z
review text: The convergence of primal and dual central paths associated with entropy and exponential functions, respectively, for semidefinite programming problems are studied in this paper. It is proven that the primal path converges to the analytic center of the primal optimal set with respect to the entropy function, the dual path converges to a point in the dual optimal set and the primal-dual path associated with these paths converges to a point in the primal-dual optimal set. As an application, the generalized proximal point method with the Kullback-Leibler distance applied to semidefinite programming problems is considered. The convergence of the primal proximal sequence to the analytic center of the primal optimal set with respect to the entropy function is established and the convergence of a particular weighted dual proximal sequence to a point in the dual optimal set is obtained.
Mathematics Subject Classification ID: 90C22
Mathematics Subject Classification ID: 90C51
zbMATH DE Number: 5633304
zbMATH Keywords: proximal point methods
zbMATH Keywords: Bregman distances
zbMATH Keywords: central path
zbMATH Keywords: semidefinite programming
reviewed by: Jean-Jacques Strodiot
MaRDI profile type: Publication
full work available at URL: s10898-008-9367-x
OpenAlex ID: W2171961288
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DOI: 10.1007/S10898-008-9367-X
description: scientific article; zbMATH DE number 5633304