A new second-order corrector interior-point algorithm for P(k)-LCP

In this paper, we propose a second-order corrector interior-point algorithm for solving P*(k)- linear complementarity problems. The method generates a sequence of iterates in a wide neighborhood of the central path introduced by Ai and Zhang. In each iteration, the method computes a corrector direction in addition to the Ai-Zhang direction, in an attempt to improve performance. The algorithm does not depend on the handicap k of the problem, so that it can be used for any P*(k)-linear complementarity problems. It is shown that the iteration complexity bound of the algorithm is O ((1+k)3 ? nL). Some numerical results are provided to illustrate the performance of the algorithm. nema