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Superlinear convergence of a predictor-corrector
method for semidefinite programming without shrinking
central path neighborhood

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Florian A. Potra and Rongqin Sheng

An infeasible start predictor-corrector algorithm for
semidefinite programming is proposed. It is a direct extension of the
Mizuno-Todd-Ye predictor-corrector algorithm for linear programming.
The algorithm uses the
Kojima-Shindoh-Hara/Helmberg-Rendl-Vanderbei-Wolkowicz/Monteiro
direction
in the predictor step and the Alizadeh-Haeberly-Overton direction
in the corrector step. It has polynomial complexity
for general problems and is
superlinearly convergent with $Q$-order at least 1.5 under strict
complementarity and nondegeneracy conditions.
Reports on Computational Mathematics, No. 91,
Department of Mathematics, The University of Iowa,
August, 1996

Contact: rsheng@math.uiowa.edu