Generalized-Hukuhara subdifferential analysis and its application in nonconvex composite interval optimization problems

Abstract

In this article, we study calculus for gH-subdifferential of convex interval-valued functions (IVFs) and apply it in a nonconvex composite model of an interval optimization problem (IOP). Towards this, we define convexity, convex hull, closedness, and boundedness of a set of interval vectors. In identifying the closedness of the convex hull of a set of interval vectors and the union of closed sets, we analyze the convergence of the sequence of interval vectors. We prove a relation on the gH-directional derivative of the maximum of finitely many comparable IVFs. With the help of existing calculus on the gH-subdifferential of an IVF, we derive a Fritz-John-type and a KKT-type efficiency condition for weak efficient solutions of IOPs. In the sequel, we analyze the supremum and infimum of a set of intervals. Further, we report a characterization of the weak efficient solutions of nonconvex composite IOPs by applying the proposed concepts. The whole analysis is supported by illustrative examples.