A trust-region approach to nonlinear systems of equalities and inequalities

In this paper, two new trust-region algorithms for the numerical solution o f systems of nonlinear equalities and inequalities are introduced. The form ulation is free of arbitrary parameters and possesses sufficient smoothness to exploit the robustness of the trust-region approach. The proposed algor ithms are one-sided least-squares trust-region algorithms. The first algori thm is a single-model algorithm, and the second one is a multimodel algorit hm where the Cauchy point computation is a model selection procedure. Global convergence analysis for the two algorithms is presented. Our analys is generalizes to nonlinear systems of equalities and inequalities the well -developed theory for nonlinear least-squares problems. Numerical experiments on the two algorithms are also presented. The perform ance of the two algorithms is reported. The numerical results validate the effectiveness of our approach.