A globally convergent filter method for nonlinear programming

Clovis C. Gonzaga (clovismtm.ufsc.br)
Elizabeth Karas (karasmat.ufpr.br)
Marcia Vanti (marcialabplan.ufsc.br)

Abstract: In this paper we present a filter algorithm for nonlinear programming and prove its global convergence to stationary points. Each iteration is composed of a restoration phase, which reduces a measure of infeasibility, and an optimality phase, which reduces the objective function in a tangential approximation of the feasible set. These two phases are totally independent, and the only coupling between them is provided by the filter. The method is independent of the internal algorithms used in each iteration, as long as these algorithms satisfy reasonable assumptions on their efficiency. The main algorithm uses no trust regions, and no properties of the linear models. Under standard hypotheses, we show two results: for a filter with minimum size, the algorithm generates a stationary accumulation point; for a slightly larger filter, all accumulation points are stationary.

Keywords: nonlinear programming, filter, global convergence

Category 1: Nonlinear Optimization (Constrained Nonlinear Optimization )

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Entry Submitted: 10/29/2001
Entry Accepted: 10/29/2001
Entry Last Modified: 04/11/2003

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