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On a general class of interior-point algorithms for semidefinite programming with polynomial complexity and superlinear convergence

We propose a unified analysis for a class of infeasible-start predictor-corrector algorithms for semidefinite programming problems, using the Monteiro-Zhang unified direction. The algorithms are direct generalizations of the Mizuno-Todd-Ye predictor-corrector algorithm for linear programming. We show that the algorithms belonging to this class are globally convergent, provided the problem has a solution, and have the best known complexity. We also give simple sufficient conditions for superlinear convergence. Our results generalize the results obtained by Potra and Sheng for the infeasible-interior-point algorithm proposed by Kojima, Shida and Shindoh and Potra and Sheng.