A quadratically convergent -iteration algorithm for the -matrix linear complementarity problem

An interior-point predictor-corrector algorithm for the -matrix linear complementarity problem is proposed. The algorithm is an extension of Mizumo-Todd-Ye's predictor-corrector algorithm for linear programming problem. The extended algorithm is quadratically convergent with iteration complexity . It is the first polynomially and quadratically convergent algorithm for a class of LCPs that are not necessarily monotone.