Penalty and Barrier Methods for Convex Semidefinite Programming

Alfred Auslender () and Héctor C. ()

Mathematical Methods of Operations Research, 2006, vol. 63, issue 2, 195-219

Abstract: In this paper we present penalty and barrier methods for solving general convex semidefinite programming problems. More precisely, the constraint set is described by a convex operator that takes its values in the cone of negative semidefinite symmetric matrices. This class of methods is an extension of penalty and barrier methods for convex optimization to this setting. We provide implementable stopping rules and prove the convergence of the primal and dual paths obtained by these methods under minimal assumptions. The two parameters approach for penalty methods is also extended. As for usual convex programming, we prove that after a finite number of steps all iterates will be feasible. Copyright Springer-Verlag 2006

Keywords: Semidefinite programming; Penalty and barrier methods; Asymptotic functions; Recession functions; Convex analysis (search for similar items in EconPapers)
Date: 2006
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DOI: 10.1007/s00186-005-0054-0

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