Geodesic B-Preinvex Functions and Multiobjective Optimization Problems on Riemannian Manifolds

Abstract

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.