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In this article, we study $gH$-subdifferential calculus of convexinterval-valued functions (IVFs) and apply it in a nonconvex composite model ofinterval optimization problems (IOPs). It is found that the $gH$-directionalderivative of maximum of finitely many comparable IVFs is the maximum of their$gH$-directional derivative. Proposed concepts of $gH$-subdifferential areobserved to be useful to derive Fritz-John-type and KKT-type efficiencyconditions for weak efficient solutions of IOPs. Further, we extract anecessary and sufficient condition to characterize the weak efficient solutionsof nonconvex composite IOPs by applying the proposed concepts. To derive theresults on $gH$-subdifferentials, the concepts of limit supremum and limitinfimum with certain properties for IVFs are defined in the sequel. The wholeanalysis is supported by appropriate expository examples.

Generalized-Hukuhara Subdifferential Analysis and Its Application in Nonconvex Composite Optimization Problems with Interval-valued Functions