A new trust-region method for solving systems of equalities and inequalities

In this paper, we propose a new trust-region method for solving nonlinear systems of equalities and inequalities. The algorithm combines both standard and adaptive trust-region frameworks to construct the steps of the algorithm. The trust-region subproblem is solved in the first iteration using a given initial radius. Then, in each iteration, the standard trust-region method is followed whenever the current trial step is accepted, otherwise, the subproblem is resolved using an adaptive scheme. The convergence results for the new proposed algorithm are established under some mild and standard assumptions. Numerical results on some least-squares test problems show the efficiency and effectiveness of the proposed algorithm in practice too.