Optimality conditions for (h, φ)-subdifferentiable multiobjective programming problems with G-type I functions

Abstract

In this paper, using generalized algebraic operations introduced by Ben-Tal [7], we introduce new classes of (h,φ)-subdifferentiable functions, called (h,φ)-G-type I functions and generalized (h,φ)-G-type I functions. Then, we consider a class of nonconvex (h, φ)-subdifferentiable multiobjective programming problems with locally Lipschitz functions in which the functions involved belong to aforesaid classes of (h, φ)-subdifferentiable nonconvex functions. For such (h, φ)-subdifferentiable vector optimization problems, we prove the sufficient optimality conditions for a feasible solution to be its (weak) Pareto solution. Further, we define a vector dual problem in the sense of Mond-Weir for the considered (h, φ)-subdifferentiable multiobjective programming problem and we prove several duality theorems for the aforesaid (h, φ)-subdifferentiable vector optimization problems also under (h, φ)-G-type I hypotheses.