Abstract: On the basis of the nonsmooth tools established on Riemannian manifolds, the nondifferentiable multiobjective optimization problems with equality and inequality constraints are extended from Euclidean space to Riemannian manifolds. Via Ekeland variational principle, the FritzJohn necessary conditions with generalized gradient formula for weak Pareto optimal solutions are derived.

Key words: multiobjective program, necessary optimality condition, generalized gradient, Riemannian manifold