A trust region filter method for general non-linear programming

Filter approach is initially proposed by Fletcher and Leyffer in 2002. Because of promising numerical results, filter methods are recently attached importance to. 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. In this paper, the filter technique is employed in a trust region algorithm. In every trial step, the step length is controlled by a trust region radius. Moreover, our purpose is not to reduce the objective function and constraint violation directly. To overcome some bad cases, we aim to reduce the degree of constraint violation and the entry of some function, and the function is a combination of the objective function and the degree of constraint violation. The algorithm in this paper requires neither Lagrangian multipliers nor strong decrease condition. In certain conditions, this method produces K–T points for the original problem. Moreover, Maratos effect can be avoided for our algorithm.