For solving nonsmooth systems of equations, the Levenberg-Marquardt method and its variants are of particular importance because of their locally fast convergent rates. Finitely manymaximum functions systems are very useful in the study of nonlinear complementarity problems, variational inequality problems, Karush-Kuhn-Tucker systems of nonlinear programming problems, and many problems in mecha...

In this article, we propose a new merit function based on sub-additive functions for solving a nonlinear complementarity problem (NCP). This leads to consider an optimization problem that is equivalent to the NCP. In the case of a concave NCP this optimization problem is a Difference of Convex (DC) program and we can therefore use DC Algorithm to locally solve it. We prove that in the case of a...

The main purpose of this paper is to investigate some kinds of nonlinear complementarity problems (NCP). For the structured tensors, such as, symmetric positive definite tensors and copositive tensors, we derive the existence theorems on a solution of these kinds of nonlinear complementarity problems. We prove that a unique solution of the NCP exists under the condition of diagonalizable tensors.

In this paper, we present a hybrid method for the solution of a class of composite semismooth equations encountered frequently in applications. The method is obtained by combining a generalized finite difference Newton method to a inexpensive direct search method. We prove that, under standard assumptions, the method is globally convergent with a local rate of convergence which is superlinear o...

In this paper, we propose and study an algorithm for a new class of complementarity problems of finding u E R” such that u > 0, Tu + A(u) > 0; (u, Tu + A(u)) = 0, where T is a continuous mapping and A is a nonlinear transformation from R” into itself. It is proved that the approximate solution obtained from the iterative scheme converges to the exact solution. Several special cases are also dis...

Extending our previous work [T. Wang, R. D. C. Monteiro, and J.-S. Pang, Math. Programming, 74 (1996), pp. 159–195], this paper presents a general potential reduction Newton method for solving a constrained system of nonlinear equations. A major convergence result for the method is established. Specializations of the method to a convex semidefinite program and a monotone complementarity problem...