Computational Experience with Ill-Posed Problems in Semidefinite Programming

Authors:
Gerald Gruber;Franz Rendl
Affiliations:
Universitöt Klagenfurt, Institut für Mathematik, Universitötsstraße 65-67, A-9020 Klagenfurt, Austria. gerald.gruber@uni-klu.ac.at;Universitöt Klagenfurt, Institut für Mathematik, Universitötsstraße 65-67, A-9020 Klagenfurt, Austria
Venue:
Computational Optimization and Applications
Year:
2002

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Abstract

Many theoretical and algorithmic results in semidefinite programming are based on the assumption that Slater's constraint qualification is satisfied for the primal and the associated dual problem. We consider semidefinite problems with zero duality gap for which Slater's condition fails for at least one of the primal and dual problem. We propose a numerically reasonable way of dealing with such semidefinite programs. The new method is based on a standard search direction with damped Newton steps towards primal and dual feasibility.