A penalty-free algorithm for solving nonlinear equality constrained optimization

In contrast to standard penalty type methods for nonlinear optimization, penalty-free type methods do not have to determine penalty parameters and have promising numerical results. So they have attracted the attention of many researchers. Filter method is a classical penalty-free method. In this paper, a different filter technique is introduced for solving nonlinear equality constrained optimization. The optimality condition of the nonlinear optimization problem is regarded as a new filter pair which is built in the backtracking line search framework. Then, the trial step size is accepted if one of the two measures in filter is improved after the search direction is determined. Under some reasonable assumptions, the global convergence of the algorithm is proved. Some preliminary numerical results are presented to show the usefulness of the proposed algorithm.