Geodesic B-preinvex functions and multiobjective optimization problems on riemannian manifolds

We introduce a class of functions called geodesic B -preinvex and geodesic B -invex functions on Riemannian manifolds and generalize the notions to the so-called geodesic quasi/pseudo B -preinvex and geodesic quasi/pseudo B -invex functions. We discuss the links among these functions under appropriate conditions and obtain results concerning extremum points of a nonsmooth geodesic B -preinvex function by using the proximal subdifferential. Moreover, we study a differentiable multiobjective optimization problem involving new classes of generalized geodesic B -invex functions and derive Kuhn-Tucker-type sufficient conditions for a feasible point to be an efficient or properly efficient solution. Finally, a Mond-Weir type duality is formulated and some duality results are given for the pair of primal and dual programming.