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.