Generalized Hukuhara Global Subdifferentiability in Interval Optimization Problems

Abstract

In this chapter, we propose the concept of generalized Hukuhara (gH)-global subdifferential for interval-valued function (IVF). To define this concept, we propose the notions of gH-lower and gH-upper global directional derivatives for IVFs. A few results on the characteristics of gH-lower and gH-upper global subdifferential are studied. Next, a result on the gH-directional derivative of the maximum of comparable IVFs is derived. In the sequel, a comparison of gH-lower subdifferential is given with gH-Fréchet subdifferential, gH-proximal subdifferential, and gH-subdifferential for IVFs. Thereafter, a necessary and sufficient condition for obtaining an efficient solution to an interval optimization problem (IOP) with the help of gH-lower global subdifferential is given. © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023.