Complete Duality for Quasiconvex and Convex Set-Valued Functions

TL;DR

This paper introduces a novel duality framework for set-valued quasiconvex and convex functions, enabling a comprehensive dual representation for these functions in mathematical analysis.

Contribution

It presents the first duality result specifically for set-valued lower semi-continuous quasiconvex and convex functions, expanding the theoretical understanding of such functions.

Findings

Derived a unique dual representation for set-valued quasiconvex functions

Extended duality principles to set-valued convex functions

Provided foundational results for future research in set-valued analysis

Abstract

This paper provides an unique dual representation of set-valued lower semi-continuous quasiconvex and convex functions. The results are based on a duality result for increasing set valued functions.