On symmetric gH-derivative: Applications to dual interval-valued optimization problems

Abstract

This paper provides a complete study on properties of symmetric gH-derivative. More precisely, a necessary and sufficient condition for the symmetric gH-differentiability of interval-valued functions is presented. Further, we clarify the relationship between the symmetric gH-differentiability and gH-differentiability. Moreover, quasi-mean value theorem, chain rule and some operations of symmetric gH-differentiable interval-valued functions are established. As applications, we develop the Mond–Weir duality theory for a class of symmetric gH-differentiable interval-valued optimization problems. Weak, strong and strict converse duality theorems are formulated and proved. Also, several examples are presented in order to support the corresponding theoretical results.