Necessary optimality conditions in a nondifferentiable mathematical programming on riemannian manifolds

In order to solve the nondifferentiable mathematical programming on Riemannian manifolds,the definitions of generalized directional derivative and generalized gradient of Lipschitz functions defined on Riemannian manifold are presented,respectively.By using tangent mapping,some properties of generalized directional derivative and generalized gradient are given.Moreover,the necessary optimality conditions in mathematical programming problem with equality and inequality constraints of Lipschitz functions are derived with the help of Ekeland variational principle on Riemannian manifolds.