Sequential Penalty Quadratic Programming Filter Methods for Nonlinear Programming

Filter approach is recently proposed by Fletcher and Leyffer in 2002 and is attached importance to. In this paper, the filter approach is used in an sequential penalty quadratic programming (S$l$QP) algorithm which is similar to that of Yuan's. In every trial step, the step length is controlled by a trust region radius. If the objective function value or the constraint violation is reduced, this step is accepted by a filter, which is the basic idea of the filter. But in this work, our purpose is not to reduce the objective function and constraint violation. We reduce the degree of constraint violation and some function, which is close related to the objective function. This algorithm requires neither Lagrangian multipliers nor the strong decrease condition. Further, in our S$l$QP filter strategy there is no requirement of large penalty parameter. This method produces K-T points for the original problem.