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On Pareto Dominance in Decomposably Antichain-Convex Sets

Author

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  • Maria Carmela Ceparano

    (University of Naples Federico II)

  • Federico Quartieri

    (University of Florence)

Abstract

The main contribution of the paper is the proof that any element in the convex hull of a decomposably antichain-convex set is Pareto dominated by at least one element of that set. Building on this result, the paper demonstrates the disjointness of the convex hulls of two disjoint decomposably antichain-convex sets, under the assumption that one of the two sets is upward. These findings are used to obtain a number of consequences on: the structure of the set of Pareto optima of a decomposably antichain-convex set; the separation of two decomposably antichain-convex sets; the convexity of the set of maximals of an antichain-convex relation; the convexity of the set of maximizers of an antichain-quasiconcave function. Emphasis is placed on the invariance of the solution set of a problem under its “convexification.” Some entailments in the field of mathematical economics of the results of the paper are briefly discussed.

Suggested Citation

  • Maria Carmela Ceparano & Federico Quartieri, 2020. "On Pareto Dominance in Decomposably Antichain-Convex Sets," Journal of Optimization Theory and Applications, Springer, vol. 186(1), pages 68-85, July.
    • Handle: RePEc:spr:joptap:v:186:y:2020:i:1:d:10.1007_s10957-020-01696-9
    DOI: 10.1007/s10957-020-01696-9
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    References listed on IDEAS

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