Vector variational-like inequalities and vector optimization problems on Riemannian manifolds
Sanyang Liu · Journal of Anhui University · 2009
The definitions of generalized directional derivative,generalized gradient,invex set and invex function definned on Riemannian manifolds were presented respectively.The relationships between invex function and quasi-invex function,as well as pseudo-invex function were given.The concepts of(weak) vector variational inequality were given.Moreover,with the conditions of invex or geodesic convex function,the rela-tionships between the solutions of(weak) vector variational inequalities and the(weak) efficient solutions of vectoroptimizations were studied.