Global and superlinear convergence of the smoothing Newton method and its application to general box constrained variational inequalities

摘要: The smoothing Newton method for solving a system of nonsmooth equations F(x) = 0, which may arise from the nonlinear complementarity problem, variational inequality problem or other problems, can be regarded as variant method. At kth step, function F is approximated by smooth f(.,∈ κ ), and derivative ) at x k used iterative matrix. merits methods are global convergence convenience in handling. In this paper, we show that also superlinearly convergent if semismooth solution f satisfies Jacobian consistency property. We most common functions, such Gabriel-More function, have As an application, box constrained inequalities involved P- uniform, iteration sequence generated will converge to unique globally (quadratically).