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Abstract: In this work we discuss global convergence of a general filter algorithm that depends neither on the definition of the forbidden region, which can be given by the original or slanting filter rule, nor on the way in which the step is computed. This algorithm basically consists of calculating a point not forbidden by the filter from the current point. Assuming that this step must be efficient, in the sense that near a feasible non-stationary point the decrease in the objective function is relatively large, we prove the global convergence of the algorithm. We also discuss that such a condition is satisfied if the step is computed by the SQP or Inexact Restoration methods. For SQP we present a general proof of this result that is valid for both the original and the slanting filter criterion. In order to compare the performance of the general filter algorithm according to the method used to calculate the step and the filter rule regarded, we present numerical experiments performed with problems from CUTEr collection. [Copyright &y& Elsevier]

Abstract: In this paper, we present a general algorithm for nonlinear programming which uses a slanting filter criterion for accepting the new iterates. Independently of how these iterates are computed, we prove that all accumulation points of the sequence generated by the algorithm are feasible. Computing the new iterates by the inexact restoration method, we prove stationarity of all accumulation points of the sequence. [Copyright &y& Elsevier]