Two Interior-point Methods for Nonlinear P ( )-complementarity Problems

1 The authors would like to thank two anonymous referees for their helpful suggestions leading to a improved presentation of the paper. Abstract. Two interior-point algorithms using a wide neighborhood of the central path are proposed to solve nonlinear P-complementarity problems. The proof of the polynomial complexity of the rst method requires that the problem satisses a scaled Lipschitz condition. When specialized to the monotone complementarity problems, the results of the rst method are similar to the ones in Ref. 1. The second method is quite diierent from the rst in that the proof of its global convergence does not require the scaled Lipschitz assumption. At each step of this algorithm, however, one has to compute an approximate solution of a nonlinear system such that a certain accuracy requirement is satissed.