Abstract
One of the important problems of vector optimization concerns the density of the set of positive proper minimal points in the set of minimal points. We use the concepts of dentable point and approximating cones to derive sufficient conditions guaranteeing that the set of minimal points is contained in the closure of the set of positive proper minimal points. The result can be applied to obtain a density result for the unit ball in 1p, 1<p<+∞, which does not follow from any other well-known density theorem.
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Communicated by H. P. Benson
The author would like to thank Professor W. T. Fu for helpful comments. Moreover, the author is grateful to Professor H. P. Benson and the referees for valuable remarks and suggestions concerning a previous draft of this paper.
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Gong, X.H. Density of the set of positive proper minimal points in the set of minimal points. J Optim Theory Appl 86, 609–630 (1995). https://doi.org/10.1007/BF02192161
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DOI: https://doi.org/10.1007/BF02192161