Local convergence of predictor-corrector infeasible-interior-point algorithms for SDPs and SDLCPs

An example of SDPs (semide nite programs) exhibits a substantial di culty in proving the superlinear convergence of a direct extension of the Mizuno-Todd-Ye type predictorcorrector primal-dual interior-point method for LPs (linear programs) to SDPs, and suggests that we need to force the generated sequence to converge to a solution tangentially to the central path (or trajectory). A Mizuno-Todd-Ye type predictor-corrector infeasible-interior-point algorithm incorporating this additional restriction for monotone SDLCPs (semide nite linear complementarity problems) enjoys superlinear convergence under strict complementarity and nondegeneracy conditions.