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

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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