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A Newton-Fixed Point Homotopy Algorithm For Nonlinear Complementarity Problems With Generalized Monotonicity

In this paper has been considered probability-one global convergence of NFPH (Newton-Fixed Point Homotopy) algorithm for system of nonlinear equations and has been proposed a probability-one homotopy algorithm to solve a regularized smoothing equation for NCP with generalized monotonicity. Our results provide a theoretical basis to develop a new computational method for nonlinear equation systems and complementarity problems. Some preliminary numerical experiments shows that our NFPH method is useful and promissing for difficult nonlinear problems.