AN INFEASIBLE PATH-FOLLOWING METHOD FOR MONOTONE COMPLEMENTARITY-PROBLEMS

We propose an infeasible path-following method for solving the monoton e complementarity problem. This method maintains positivity of the ite rates and uses two Newton steps per iteration-one with a centering ter m for global convergence and one without the centering term for local superlinear convergence. We show that every cluster point of the itera tes is a solution, and if the underlying function is affine or is suff iciently smooth and a uniform nondegenerate function on R-++(n), then the convergence is globally Q-linear. Moreover, if every solution is s trongly nondegenerate, the method has local quadratic convergence. The iterates are guaranteed to be bounded when either a Slater-type feasi ble solution exists or when the underlying function is an R-0-Function .