Strong duality and minimal representations for cone optimization
Computational Optimization and Applications
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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. 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 Alizadeh--Haeberly--Overton (AHO) direction since there the scaling matrix is the identity matrix.