On the convergence of a trust-region method for solving constrained nonlinear equations with degenerate solutions (Q1771108)

The authors discuss a so called trust-region method for the numerical solving of a system of constrained nonlinear equations. The new method can be regarded as an extension of the work of the authors [ibid. 120, No. 3, 601--625 (2004; Zbl 1140.65331)] and of the method of \textit{C. Kanzow} [Complementarity: Applications, Algorithms and Extensions (Kluwer Academic Publishers, Dordrecht), 179--200 (2001; Zbl 0983.90060)]. The proposed method is globally convergent. Local superlinear and quadratic convergence of the algorithm under the condition of a local error bound, are proved. Eight numerical examples taken from the literature are performed by the proposed method, and the results are promising. In most of the examples, the iterative sequence converges to the solution quickly.