Mathematical Programming 62 (1993) 537-551 537 North-Holland On quadratic and O( L) convergence of a predictor-corrector algorithm for LCP Yinyu Ye* and Kurt Anstreicher Department of Management Sciences, University of lowa, Iowa City, IA, USA Received 3 December 1991 Revised manuscript received 20 September 1992 Recently several new results have been developed for the asymptotic (local) convergence of polynomial-time interior-point algorithms. It has been shown that the predictor-corrector algorithm for linear programming (LP) exhibits asymptotic quadratic convergence of the primal~lual gap to zero, without any assumptions concerning nondegeneracy, or the convergence of the iteration sequence. In this paper we prove a similar result for the monotone linear complementarity problem (LCP), assuming only that a strictly complementary solution exists. We also show by example that the existence of a strictly complementarity solution appears to be necessary to achieve superlinear convergence for the algorithm. Key words." Linear complementarity problem, quadratic programming, superlinear convergence, quadratic con- vergence, polynomial-time algorithm. 1. Introduction Consider the linear complementarity problem (LCP): min xTs s.t. s=Mx+q, (x, s)>~O, where M~ ~n × n and q ~ ~n. As usual, we assume without losing generality: (A1) The feasible region of LCP has a nonempty relative interior, i.e., there exists (x °, s °) such that s o =Mx ° + q and x ° > 0, s o > 0. Note that M may not be symmetric. However, for (x, s) feasible in LCP, the objective may be written as x Xs = ½xv (M + M T) x + q Xx, and M + M x is symmetric. The LCP problem is called monotone (convex) if and only if M+M x is positive semi-definite, which we assume throughout this paper: Correspondence to: Prof. Yinyu Ye, Department of Management Sciences, University of Iowa, Iowa City, IA 52242, USA. *Research supported in part by NSF Grants DDM-8922636 and DDM-9207347, and an Interdisciplinary Research Grant of the University of Iowa, Iowa Center for Advanced Studies.