Please use this identifier to cite or link to this item: https://dspace.ctu.edu.vn/jspui/handle/123456789/71575
Title: Sectional convexity of epigraphs of conjugate mappings with applications to robust vector duality
Authors: Nguyen, Dinh
Dang, Hai Long
Keywords: Robust vector optimization
Robust convex optimization
Robust convex strong duality
Robust stable vector Parkas lemma
Sectionally convex sets
Sectionally closed sets
Issue Date: 2020
Series/Report no.: Acta Mathematica Vietnamica;Vol.45, No.02 .- P.525-553
Abstract: This paper concerns the robust vector problem (RVP) W Min { F(x) : x € C. G„ (x) є -S, V« є U. where X, Y. Z are locally convex Hausdorff topological vector spaces, K is a closed and convex cone in Y with a nonempty interior, and S is a closed, convex cone in Z, U is an uncertainty set, F : X —> Y*, G„ : X —> Z* are proper mappings for all u € U. and θ ≠ C ⊂ X. The results then give rise to stable robust vector/convex vector Farkas lemmas which, in turn, are used to establish new results on robust strong stable duality results for (RVP). It is shown at the end of the paper that, when specifying the result to some concrete classes of scalar robust problems (i.e., when Y = R), our results cover and extend several corresponding known ones in the literature.
URI: https://dspace.ctu.edu.vn/jspui/handle/123456789/71575
ISSN: 0251-4184
Appears in Collections:Acta Mathematica Vietnamica 

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