A non-monotone variant of the trust-region SQP-filter algorithm analyzed in Fletcher, Gould, Leyffer, Toint and Wachter (2002a) that directly uses the dominated area of the filter as an acceptability criterion for trial points is defined. It is proved that, under reasonable assumptions and for all possible choices of the starting point, the algorithm generates at least a subsequence converging to a first-order critical point.
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