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

An example of an SDP (semidefinite program) exhibits a substantial difficulty in proving the superlinear convergence of a direct extension of the Mizuno–Todd–Ye type predictor–corrector 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 (semidefinite linear complementarity problems) enjoys superlinear convergence under strict complementarity and nondegeneracy conditions.