On the convergence of a trust-region method for solving constrained nonlinear equations with degenerate solutions

This paper presents a trust-region method for solving the constrained nonlinear equation F(x) = 0, x is an element of Omega, where Omega subset of R(n) is a nonempty and closed convex set, F is defined on an open set containing Omega and is continuously differentiable. The iterates generated by the method are feasible. The method is globally and quadratically convergent under local error bounded assumption on F. The results obtained are extensions of the work of Yamashita and Fukushima (Ref. 1) and Fan and Yuan (Ref. 2) for unconstrained nonlinear equations. Numerical results show that the new algorithm works quite well.