On a General Class of Interior-point Algorithms for Semideenite Programming with Polynomial Complexity and Superlinear Convergence

We propose a uniied analysis for a class of infeasible-start predictor-corrector algorithms for semideenite programming problems, using the Monteiro-Zhang uniied 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 optimal computational complexity. We also give simple suucient conditions for super-linear convergence. Our results generalize the results obtained by the rst two authors for the infeasible-interior-point algorithm proposed by Kojima, Shida and Shindoh and Potra and Sheng. Abbreviated Title: On a general class of algorithms for SDP.