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

Maria Carmela Ceparano; Federico Quartieri

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arXiv · 1909.00402

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

Maria Carmela Ceparano·Federico Quartieri

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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 $C$-antichain-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".

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Maria Carmela Ceparano, Federico Quartieri. 2019-09-01. On $C$-Pareto dominance in decomposably $C$-antichain-convex sets. https://arxiv.org/abs/1909.00402

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