CDT like approaches for the system of nonlinear equations

In this paper, Celis-Dennis-Tapia (C-D-T or CDT) subproblem approach, is given a new use and is employed to tackle the system of nonlinear equations. In the new method, the system of nonlinear equations is transferred into a constrained nonlinear programming problem, which is then solved by C-D-T subproblem algorithms. We handle a C-D-T subproblem to obtain a trial step. Some criterion, similar to that in the trust region technique, is then employed to determine whether to accept this trial point or not. In the new algorithm, an ϵ approximate solution or an locally infeasible point is obtained. In essence, constrained optimization methods are utilized to cope with the system of nonlinear equations.