A Brief History of Filter Methods∗

We consider the question of global convergence of iterative methods for nonlinear programming problems. Traditionally, penalty functions have been used to enforce global convergence. In this paper we review a recent alternative, so-called filter methods. Instead of combing the objective and constraint violation into a single function, filter methods view nonlinear optimization as a biobjective optimization problem that minimizes the objective and the constraint violation. We outline the main ideas and convergence results of filter methods and indicate other areas where filter methods have been used successfully.