Clarke subdifferential, Pareto-Clarke critical points and descent directions to multiobjective optimization on Hadamard manifolds

Abstract

In this paper, we aim to complement our work reported in [20] by showing some further properties and results on Clarke subdifferential, Pareto-Clarke critical points and descent directions on Hadamard manifolds. These tools and results can be applied to introduce new algorithms for solving nonsmooth nonconvex multiobjective minimization problems on Hadamard manifolds.