Gonzaga, Clóvis C.; Karas, Elizabeth; Vanti, Márcia A globally convergent filter method for nonlinear programming. (English) Zbl 1079.90129 SIAM J. Optim. 14, No. 3, 646-669 (2003). Summary: We present a filter algorithm for nonlinear programming and prove its global convergence to stationary points. Each iteration is composed of a feasibility 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. 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. Cited in 2 ReviewsCited in 57 Documents MSC: 90C30 Nonlinear programming 49M37 Numerical methods based on nonlinear programming 65K05 Numerical mathematical programming methods Keywords:filter methods; nonlinear programming; global convergence PDFBibTeX XMLCite \textit{C. C. Gonzaga} et al., SIAM J. Optim. 14, No. 3, 646--669 (2003; Zbl 1079.90129) Full Text: DOI