A Trust Region Method for Constrained Nonsmooth Equations

In this paper, we develop and analyze the convergence of a fairly general trust region method for solving a system of nonsmooth equations subject to some linear constraints. The method is based on the existence of an iteration function for the nonsmooth equations and involves the solution of a sequence of sub- problems defined by this function. A particular realization of the method leads to an arbitrary-norm trust region method. Applications of the latter method to the nonlinear complementarity and related problems are discussed. Sequential convergence of the method and its rate of convergence are established under certain regularity conditions similar to those used in the NE/SQP method [14] and its generalization [16]. Some computational results are reported.