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Penalty and Barrier Methods for Convex Semidefinite Programming

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  • Alfred Auslender
  • Héctor C.

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

Suggested Citation

  • Alfred Auslender & Héctor C., 2006. "Penalty and Barrier Methods for Convex Semidefinite Programming," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 63(2), pages 195-219, May.
    • Handle: RePEc:spr:mathme:v:63:y:2006:i:2:p:195-219
    DOI: 10.1007/s00186-005-0054-0
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    References listed on IDEAS

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    1. A. Auslender & R. Cominetti & M. Haddou, 1997. "Asymptotic Analysis for Penalty and Barrier Methods in Convex and Linear Programming," Mathematics of Operations Research, INFORMS, vol. 22(1), pages 43-62, February.
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