On $C$-Pareto dominance in decomposably $C$-antichain-convex sets

Abstract

This paper shows that-under suitable conditions on a cone C-any element in the convex hull of a decomposably C-antichain-convex set Y is C-Pareto dominated by some element of Y . Building on this, the paper proves the disjointness of the convex hulls of two disjoint decomposably Cantichain-convex sets whenever one of latter is C-upward. These findings are used to obtain several consequences on the structure of the C-Pareto optima of decomposably C-antichain-convex sets, on the separation of decomposably C-antichain-convex sets and on the convexity of the set of maximals of C-antichain-convex relations and of the set of maximizers of C-antichain-quasiconcave functions. Special emphasis is placed on the invariance of the solution set of a problem after its "convexification".