Abstract
In this paper, we introduce a new class of functions called roughly geodesic B - r- preinvex function on a Hadamard manifold and establish some properties of roughly geodesic B - r- preinvex functions on Hadamard manifolds. It is observed that a local minimum point for a scalar optimization problem is also a global minimum point under roughly geodesic B-r- preinvexity on the Hadamard manifolds. The results presented in this paper extend to and generalize the results in the literature.