Sufficient Optimality Conditions on Riemannian Manifolds

This paper is intended to motivate our investigation of sufficient conditions for the point x to be a strict local minimizer of the vector-valued function f: N-XY, where N is a subset ofRiemannian manifold M and Y is a normed space. For this purpose, we need some new definitions on Riemannian manifolds such as the contingent cone to a closed subset S of Riemannian manifoldMat a point x e S.

Keywords:

Riemannian manifold , Vector Optimization , Strict local minimum , First order sufficientoptimality condition , Support function