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arXiv · 2109.11516

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

Krishan Kumar·Debdas Ghosh·Gourav Kumar
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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.

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Krishan Kumar, Debdas Ghosh, Gourav Kumar. 2021-09-23. Weak sharp minima for interval-valued functions and its primal-dual characterizations using generalized Hukuhara subdifferentiability. https://arxiv.org/abs/2109.11516

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