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This paper is aimed at establishing a conjugate duality for the constrained optimizations equipped with some topical structures. First, we provide a dual problem for the general constrained optimization, discussing the weak duality as well as the strong duality based on the theory of abstract convexity. Transforming the zero duality gap property into a separation of two sets in image space, we involve...
In this paper, we consider some scalarization functions, which consist of the generalized min-type function, the so-called plus-Minkowski function and their convex combinations. We investigate the abstract convexity properties of these scalarization functions and use them to identify the maximal points of a set in an ordered vector space. Then, we establish some versions of Farkas type results for...
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