On $C$Pareto dominance in decomposably $C$antichainconvex sets
Abstract
This paper shows thatunder suitable conditions on a cone $C$any element in the convex hull of a decomposably $C$antichainconvex 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 $C$antichainconvex 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 $C$antichainconvex sets, on the separation of decomposably $C$antichainconvex sets and on the convexity of the set of maximals of $C$antichainconvex relations and of the set of maximizers of $C$antichainquasiconcave functions. Special emphasis is placed on the invariance of the solution set of a problem after its "convexification".
 Publication:

arXiv eprints
 Pub Date:
 September 2019
 arXiv:
 arXiv:1909.00402
 Bibcode:
 2019arXiv190900402C
 Keywords:

 Mathematics  Optimization and Control;
 52A01 (Primary);
 54F05;
 58E17 (Secondary)
 EPrint:
 25 pages