Predictor-corrector algorithm for solving P*(k)-matrix LCP from arbitrary positive starting points

A new predictor-corrector algorithm is proposed for solving P ()-matrix linear complementarity problems. If the problem is solvable, then the algorithm converges from an arbitrary positive starting point (x 0 ; s 0). The computational complexity of the algorithm depends on the quality of the starting point. If the starting point is feasible or close to being feasible, it has O((1+) p n== 0 L)-iteration complexity, where 0 is the ratio of the smallest and average coordinate of X 0 s 0. With appropriate initialization, a modiied version of the algorithm terminates in O((1 +) 2 (n== 0)L) steps either by nding a solution or by determining that the problem is not solvable. The algorithm is quadratically convergent for problems having a strictly complementary solution. We also propose an extension of a recent algorithm of Mizuno to P ()-matrix linear complementarity problems such that it can start from arbitrary positive points and has superlinear convergence without a strictly complementary condition.