On the convergence of the central path in semidefinite optimization

Margareta Halicka (halickafmph.uniba.sk)
Etienne De Klerk (E.deKlerkits.tudelft.nl)
Cornelis Roos (C.Roosits.tudelft.nl)

Abstract: The central path in linear optimization always converges to the analytic center of the optimal set. This result was extended to semidefinite programming by Goldfarb and Scheinberg (SIAM J. Optim. 8: 871-886, 1998). In this paper we show that this latter result is not correct in the absence of strict complementarity. We provide a counterexample, where the central path converges to a different optimal solution. This unexpected result raises many questions. We also give a rigorous proof that the central path always converges in semidefinite optimization, by using ideas from algebraic geometry.

Keywords: Semidefinite optimization, linear optimization, interior point method

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Category 2: Linear, Cone and Semidefinite Programming

Category 3: Nonlinear Optimization

Citation: Technical report Faculty ITS, Delft University of Technology Mekelweg 4, 2628 CD Delft, The Netherlands

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Entry Submitted: 06/27/2001
Entry Accepted: 06/27/2001
Entry Last Modified: 06/27/2001

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