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In this paper, we propose nonlinear conjugate gradient methods for vectoroptimization on Riemannian manifolds. The concepts of Wolfe and Zoutendjikconditions are extended for Riemannian manifolds. Specifically, we establishthe existence of intervals of step sizes that satisfy the Wolfe conditions. Theconvergence analysis covers the vector extensions of the Fletcher--Reeves,conjugate descent, and Dai--Yuan parameters. Under some assumptions, we provethat the sequence obtained by the algorithm can converge to a Pareto stationarypoint. Moreover, we also discuss several other choices of the parameter.Numerical experiments illustrating the practical behavior of the methods arepresented.

Nonlinear conjugate gradient method for vector optimization on Riemannian manifolds with retraction and vector transport