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arXiv · 2104.07497

Generalized-Hukuhara Subgradient and its Application in Optimization Problem with Interval-valued Functions

Amit Kumar Debnath·Debdas Ghosh·Radko Mesiar·Ram Surat Chauhan
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Abstract

In this article, the concepts of gH-subgradients and gH-subdifferentials of interval-valued functions are illustrated. Several important characteristics of the gH-subdifferential of a convex interval-valued function, e.g., closeness, boundedness, chain rule, etc. are studied. Alongside, we prove that gH-subdifferential of a gH-differentiable convex interval-valued function only contains gH-gradient of that interval-valued function. It is observed that the gH-directional derivative of a convex interval-valued function in each direction is maximum of all the products of gH-subgradients and the direction. Importantly, we show that a convex interval-valued function is gH-Lipschitz continuous if it has gH-subgradients at each point in its domain. Furthermore, the relations between efficient solutions of an optimization problem with interval-valued function and its gH-subgradients are derived.

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Amit Kumar Debnath, Debdas Ghosh, Radko Mesiar, Ram Surat Chauhan. 2021-04-15. Generalized-Hukuhara Subgradient and its Application in Optimization Problem with Interval-valued Functions. https://arxiv.org/abs/2104.07497

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