Weak sharp minima for interval-valued functions and its primal-dual characterizations using generalized Hukuhara subdifferentiability

TL;DR

This paper develops primal and dual characterizations of weak sharp minima for convex interval-valued functions using generalized Hukuhara subdifferentiability and directional derivatives.

Contribution

It introduces the concept of weak sharp minima for convex IVFs and provides primal and dual characterizations using $gH$-derivatives and subdifferential calculus.

Findings

Characterization of WSM for convex IVFs

Development of $gH$-subdifferential calculus

Dual descriptions of WSM set

Abstract

This article introduces the concept of weak sharp minima (WSM) for convex interval-valued functions (IVFs). To identify a set of WSM of a convex IVF, we provide its primal and dual characterizations. The primal characterization is given in terms of $gH$-directional derivatives. On the other hand, to derive dual characterizations, we propose the notions of the support function of a subset of $I(\mathbb{R})^{n}$ and $gH$-subdifferentiability for convex IVFs. Further, we develop the required $gH$-subdifferential calculus for convex IVFs. Thereafter, by using the proposed $gH$-subdifferential calculus, we provide dual characterizations for the set of WSM of convex IVFs.