On the local convergence of a predictor-corrector method for semidefinite programming

Jun Ji, Florian A. Potra and Rongqin Sheng

We study the local convergence of a predictor-corrector algorithm for semidefinite programming problems based on the Monteiro-Zhang unified direction whose polynomial convergence was recently established by Monteiro. We prove that the sufficient condition for superlinear convergence of Potra and Sheng applies to this algorithm and is independent of the scaling matrices. Under strict complementarity and nondegeneracy assumptions superlinear convergence with $Q$-order 1.5 is proved if the scaling matrices in the corrector step have bounded condition number. A version of the predictor-corrector algorithm enjoys quadratic convergence if the scaling matrices in both predictor and corrector steps have bounded condition numbers. The latter results apply in particular to algorithms using the AHO direction since there the scaling matrix is the identity matrix.

REPORTS ON COMPUTATIONAL MATHEMATICS, NO. 98/1997, DEPARTMENT OF MATHEMATICS, THE UNIVERSITY OF IOWA

Contact: potra@math.uiowa.edu

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