Existence and Lagrangian duality for maximizations of set-valued functions
Journal of Optimization Theory and Applications
An existence theorem in vector optimization
Mathematics of Operations Research
Choquet boundaries and efficiency
Computers & Mathematics with Applications
Characterizing efficiency without linear structure: a unified approach
Journal of Global Optimization
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In a set without linear structure equipped with a preorder, we give a general existence result for efficient points. In a topological vector space equipped with a partial order induced by a closed convex cone with a bounded base, we prove another kind of existence result for efficient points; this result does not depend on the Zorn lemma. As applications, we study a solution problem in vector optimization and generalize the Bishop--Phelps theorem to a topological vector space setting by showing that the B-support points of any sequentially complete closed subset A of a topological vector space E is dense in ∂A, where B is any bounded convex subset of E.