Optimality conditions and duality for nondifferentiable multiobjective programming problems involving d-r-type I functions

In this paper, new classes of nondifferentiable functions constituting multiobjective programming problems are introduced. Namely, the classes of d$d$-r$r$-type I objective and constraint functions and, moreover, the various classes of generalized d$d$-r$r$-type I objective and constraint functions are defined for directionally differentiable multiobjective programming problems. Sufficient optimality conditions and various Mond–Weir duality results are proved for nondifferentiable multiobjective programming problems involving functions of such type. Finally, it is showed that the introduced d$d$-r$r$-type I notion with r≠0$r\ne 0$ is not a sufficient condition for Wolfe weak duality to hold. These results are illustrated in the paper by suitable examples.