Weak sharp minima for interval-valued functions and its primal-dual characterizations using generalized Hukuhara subdifferentiability
Year: 2021
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Kumar, Krishan, Ghosh, Debdas, Kumar, Gourav
Institutions: Indian Institute of Technology BHU, Banaras Hindu University
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4298077646