A Mehrotra-type predictor-corrector algorithm with polynomiality andQ-subquadratic convergence

Abstract

Mehrotra's predictor-corrector algorithm [3] is currently considered to be one of the most practically efficient interior-point methods for linear programming. Recently, Zhang and Zhang [18] studied the global convergence properties of the Mehrotra-type predictor-corrector approach and established polynomial complexity bounds for two interior-point algorithms that use the Mehrotra predictor-corrector approach. In this paper, we study the asymptotic convergence rate for the Mehrotra-type predictor-corrector interior-point algorithms. In particular, we construct an infeasible-interior-point algorithm based on the second algorithm proposed in [18] and show that while retaining a complexity bound ofO(n1.5t)-iterations, under certain conditions the algorithm also possesses aQ-subquadratic convergence, i.e., a convergence ofQ-order 2 with an unboundedQ-factor.