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A new ABB theorem in normed vector spaces. (English) Zbl 1055.90064
Authors’ summary: We extend the Arrow, Barankin and Blackwell (ABB) theorem for Henig efficient points for nonconvex sets in normed vector spaces. The novelty of our result is especially represented by the fact that we do not assume compactness of the set; in fact it can be an unbounded asymptotically compact set. Our result subsumes several generalizations of this important theorem.

MSC:
90C29 Multi-objective and goal programming
90C30 Nonlinear programming
49J27 Existence theories for problems in abstract spaces
90C48 Programming in abstract spaces
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