Extremality of families of sets and set-valued optimization

TL;DR

This paper introduces a new extremality model for families of sets, enhancing set-valued optimization by relaxing assumptions and simplifying proofs, thus broadening the applicability of existing theories.

Contribution

It proposes a novel extremality framework applicable to arbitrary set families, improving upon prior models in set-valued optimization.

Findings

Applicable to general preferences in set-valued optimization

Weakens assumptions of existing extremality results

Provides streamlined proofs for the extremality model

Abstract

The paper explores a new extremality model involving collections of arbitrary families of sets. We demonstrate its applicability to set-valued optimization problems with general preferences, weakening the assumptions of the known results and streamlining their proofs.