Economics at your fingertips  

On Pareto Dominance in Decomposably Antichain-Convex Sets

Maria Carmela Ceparano () and Federico Quartieri
Additional contact information
Maria Carmela Ceparano: University of Naples Federico II

Journal of Optimization Theory and Applications, 2020, vol. 186, issue 1, No 4, 68-85

Abstract: 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.

Keywords: Generalized convexity; Pareto dominance; Maximal; Separation; 52A01; 54F05; 58E17 (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: Track citations by RSS feed

Downloads: (external link) Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link:

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-020-01696-9

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().

Page updated 2021-09-17
Handle: RePEc:spr:joptap:v:186:y:2020:i:1:d:10.1007_s10957-020-01696-9