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

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