A NEW TRUST-REGION ALGORITHM FOR NONLINEAR CONSTRAINED OPTIMIZATION

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 aquadratic approximation to the augmented Lagrange function in the trust region.Theaugmented Lagrange function is also used as a merit function to decide whether the trialstep should be accepted.Our method extends the traditional trust region approach bycombining a filter technique into the rules for accepting trial steps so that a trial stepcould still be accepted even when it is rejected by the traditional rule based on merit functionreduction.An estimate of the Lagrange multiplier is updated at each iteration,andthe penalty parameter is updated to force sufficient reduction in the norm of the constraintviolations.Active set technique is used to handle the inequality constraints.Numericalresults for a set of constrained problems from the CUTEr collection are also reported.