Abstract
Abstract In this paper, a new improved smoothing Newton algorithm for the nonlinear complementarity problem was proposed. This method has two-fold advantages. First, compared with the classical smoothing Newton method, our proposed method needn’t nonsingular of the smoothing approximation function; second, the method also inherits the advantage of the classical smoothing Newton method, it only needs to solve one linear system of equations at each iteration. Without the need of strict complementarity conditions and the assumption of P0 property, we get the global and local quadratic convergence properties of the proposed method. Numerical experiments show that the efficiency of the proposed method.
Highlights
Consider the following nonlinear complementarity problems, x ≥, F(x) ≥, xTF(x) =, (1.1)where F := (F, F, . . . , Fn)T, and F : n → n is continuously di erentiable function
It is obvious that smoothing functions play a very important role in smoothing methods
Based on the smoothing functions, scholars proposed a number of smoothing algorithms
Summary
Levenberg-Marquardt method is proposed for solving nonlinear complementarity problems with P function in [14]. Based on a partially smoothing function, Wan et al.[15] proposed a partially smoothing Jacobian method for solving the nonlinear complementarity problems. In this paper, motivated by the above work, we propose an improved smoothing Newton method for solving the Problem (1.1). Without strict complementarity conditions and the assumption of P property, we prove that the proposed smoothing method possess the global and local quadratic convergence properties.
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