On optimality conditions and duality for non-differentiable interval-valued programming problems with the generalized (F; ρ)-convexity

Abstract

Because interval-valued programming problem is used to tackle interval uncertainty that appears in many mathematical or computer models of some deterministic real-world phenomena, this paper considers a non- differentiable interval-valued optimization problem in which objective and all constraint functions are interval-valued functions, and the involved endpoint functions in interval-valued functions are locally Lipschitz and Clarke sub- differentiable. A necessary optimality condition is first established. Some suffcient optimality conditions of the considered problem are derived for a feasible solution to be an effcient solution under the G - (F; ρ) convexity assumption. Weak, strong, and converse duality theorems for Wolfe and Mond-Weir type duals are also obtained in order to relate the effcient solution of primal and dual inter-valued programs.