Convex optimization of interval valued functions on mixed domains

Abstract

In this paper, we study a class of convex type interval-valued functions on the domain of the product of closed subsets of real numbers. By considering $LW$ order relation on the class of closed intervals, we proposed some optimal solutions. $LW$ convexity concepts and generalized Hukuhara differentiability (viz. delta and nabla) for interval-valued functions yield the necessary and sufficient conditions for interval programming problem. In addition, we compare our results with the results given in the literature. These results may open a new avenue for modeling and solve a different type of optimization problems that involve both discrete and continuous variables at the same time.