(untitled) (Journal of Computational Mathematics, 2018)
We propose a new trust region algorithm for nonlinear constrained optimization problems. In each iteration of our algorithm, the trial step is computed by minimizing a quadratic approximation to the augmented Lagrange function in the trust region. The augmented Lagrange function is also used as a merit function to decide whether the trial step should be accepted. Our method extends the traditional trust region approach by combining a filter technique into the rules for accepting trial steps so that a trial step could still be accepted even when it is rejected by the traditional rule based on merit function reduction. An estimate of the Lagrange multiplier is updated at each iteration, and the penalty parameter is updated to force sufficient reduction in the norm of the constraint violations. Active set technique is used to handle the inequality constraints. Numerical results for a set of constrained problems from the CUTEr collection are also reported.