A quadratically convergent $$O((\kappa + 1)\sqrt n L)$$ -iteration algorithm for theP *(κ)-matrix linear complementarity problem

Abstract

An interior-point predictor-corrector algorithm for theP *(κ)-matrix linear complementarity problem is proposed. The algorithm is an extension of Mizuno—Todd—Ye's predictor—corrector algorithm for linear programming problem. The extended algorithm is quadratically convergent with iteration complexity $$O((\kappa + 1)\sqrt n L)$$ . It is the first polynomially and quadratically convergent algorithm for a class of LCPs that are not necessarily monotone.