Optimality and Duality for Interval-Valued Vector Problems

Our goal in this paper is to retain the ideology of convexificators to construct adequate Fritz John and KKT optimality conditions for nonsmooth programming problems with local weakly LU-Pareto solutions having inequality, equality, and set constraints in Banach space where the involved functions admit convexificators. Sufficiency criteria for local weakly LU-Pareto solutions have been formulated under suitable conditions on the generalized convexity. The desired duality theorems have been proposed for both Mond-Weir dual problems (MDCIMP) and Wolfe-type dual problems (WDCIMP). Numerical examples are constructed to justify the methodology adopted in the paper. Our paper extends some of the recently published articles to a great extent.