THE GENERALIZED CONDITIONAL GRADIENT METHOD FOR COMPOSITE MULTIOBJECTIVE OPTIMIZATION PROBLEMS ON RIEMANNIAN MANIFOLDS

In this paper, we consider a class of composite multiobjective optimization problems, subject to a closed convex constraint set, defined on Riemannian manifolds. To tackle this problem, we propose the generalized conditional gradient method with two step size strategies, including Armijo step size and the nonmonotone line search step size. Under some reasonable conditions, the global convergence result is established, and the iteration-complexity bound for composite multiobjective optimization problems is presented on Riemannian manifolds.