A combined filter line search and trust region method for nonlinear programming

Abstract

A framework for solving a class of nonlinear programming problems via the filter method is presented. The proposed technique first solve a sequence of quadratic programming subproblems via line search strategy and to induce global convergence, trial points are accepted provided there is a sufficient decrease in the objective function or constraints violation function. In the event when the step size has reached a minimum threshold such that the trial iterate is rejected by the filter, the algorithm temporarily exits to a trust region based algorithm to generate iterates that approach the feasible region and also acceptable to the filter. Computational results on selected large scale CUTE problems on the prototype code fiILS are very encouraging and numerical performance with LOQO and SNOPT show that the algorithm is efficient and reliable.