Fréchet subdifferential calculus for interval-valued functions and its applications in nonsmooth interval optimization

Abstract

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.