FREĆHET SUBDIFFERENTIAL CALCULUS FOR INTERVAL-VALUED FUNCTIONS AND ITS APPLICATIONS IN NONSMOOTH INTERVAL OPTIMIZATION - Kumar, Gourav; Yao, Jen-Chih (Biemdas Academic Publishers, 2023)
To deal with nondifferentiable interval-valued functions (IVFs) (not necessarily convex), we present the notion of Fréchet subdifferentiability or gH-Fréchet subdifferentiability. We explore its relationship with gH-differentiability and develop various calculus results for gH-Fréchet subgradients of extended IVFs. By using the proposed notion of subdifferentiability, we derive new necessary optimality conditions for unconstrained interval optimization problems (IOPs) with nondifferentiable IVFs. We also provide a necessary condition for unconstrained weak sharp minima of an extended IVF in terms of the proposed notion of subdifferentiability. Examples are pesented to support the main results.
This paper published with affiliation IIT (BHU), Varanasi in open access mode.
Keywords: gH-Fréchet subgradient; Interval optimization; Interval-valued functions; Weak efficient solution; Weak sharp minima; Frechet; Gh-frechet subgradient; Interval optimization