A Subgradient Method for Multiobjective Optimization on Riemannian Manifolds

In this paper, a subgradient-type method for solving nonsmooth multiobjective optimization problems on Riemannian manifolds is proposed and analyzed. This method extends, to the multicriteria case, the classical subgradient method for real-valued minimization proposed by Ferreira and Oliveira (J. Optim. Theory Appl. 97:93–104, 1998). The sequence generated by the method converges to a Pareto optimal point of the problem, provided that the sectional curvature of the manifold is nonnegative and the multicriteria function is convex.