Anshika, Krishan Kumar, Debdas Ghosh, Generalized Hukuhara Dini Hadamard $\epsilon$-subdifferential and $H_{\epsilon}$-subgradient and their applications in interval optimization

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DOI: 10.23952/jano.6.2024.2.02
Volume 6, Issue 2, 1 August 2024, Pages 177-202

Abstract. In this paper, we develop and analyze the concepts of gH-Dini Hadamard $\epsilon$ -subdifferential and $H_{\epsilon}$ -subgradient for interval-valued functions (IVFs). Some important characteristics of gH-Dini Hadamard $\epsilon$ -subdifferential such as closedness, convexity, and monotonicity are studied. The interrelations between gH-subgradient and gH-Dini Hadamard $\epsilon$ -subgradient, and between gH-Fr\’echet derivative and gH-Dini Hadamard $\epsilon$ -subdifferential are investigated. To define the concept of $H_{\epsilon}$ -subgradient, the notions of the sponge of a set around a point and gH-calm IVF at a point are studied. A variational description of gH-Dini Hadamard $\epsilon$ -subgradient with $H_{\epsilon}$ -subgradient is proposed. Various necessary and sufficient conditions for obtaining an $\epsilon$ -efficient solution to an interval optimization problem (IOP) with the help of gH-Dini Hadamard $\epsilon$ -subgradient of an IVF are derived. Lastly, an application of proposed results is discussed in the sparsity regularizer for IOPs.

How to Cite this Article:
Anshika, K. Kumar, D. Ghosh, Generalized Hukuhara Dini Hadamard $\epsilon$ -subdifferential and $H_{\epsilon}$ -subgradient and their applications in interval optimization, J. Appl. Numer. Optim. 6 (2024), 177-202.