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. © 2014 sheng-lan chen et al.