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In this article, we introduce the idea of $gH$-weak subdifferential forinterval-valued functions (IVFs) and show how to calculate $gH$-weaksubgradients. It is observed that a nonempty $gH$-weak subdifferential set isclosed and convex. In characterizing the class of functions for which the$gH$-weak subdifferential set is nonempty, it is identified that this class isthe collection of $gH$-lower Lipschitz IVFs. In checking the validity of sumrule of $gH$-weak subdifferential for a pair of IVFs, a counterexample isobtained, which reflects that the sum rule does not hold. However, under a mildrestriction on one of the IVFs, one-sided inclusion for the sum rule holds.Next, as applications, we employ $gH$-weak subdifferential to provide a fewoptimality conditions for nonsmooth IVFs. Further, a necessary optimalitycondition for interval optimization problems with difference of two nonsmoothIVFs as objective is established. Lastly, a necessary and sufficient conditionvia augmented normal cone and $gH$-weak subdifferential of IVFs for findingweak efficient point is presented.

Generalized Hukuhara Weak Subdifferential and its Application on Identifying Optimality Conditions for Nonsmooth Interval-valued Functions