GENERALIZED HUKUHARA DINI HADAMARD ε-SUBDIFFERENTIAL AND Hε-SUBGRADIENT AND THEIR APPLICATIONS IN INTERVAL OPTIMIZATION

Abstract

In this paper, we develop and analyze the concepts of gH-Dini Hadamard ε-subdifferential and Hε-subgradient for interval-valued functions (IVFs). Some important characteristics of gH-Dini Hadamard ε-subdifferential such as closedness, convexity, and monotonicity are studied. The interrelations between gH-subgradient and gH-Dini Hadamard ε-subgradient, and between gH-Fréchet derivative and gH-Dini Hadamard ε-subdifferential are investigated. To define the concept of Hε-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 gHDini Hadamard ε-subgradient with Hε-subgradient is proposed. Various necessary and sufficient conditions for obtaining an ε-efficient solution to an interval optimization problem (IOP) with the help of gH-Dini Hadamard ε-subgradient of an IVF are derived. Lastly, an application of proposed results is discussed in the sparsity regularizer for IOPs. © 2024 Journal of Applied and Numerial Optimization.