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We study the convergence issue for inexact descent algorithm (employinggeneral step sizes) for multiobjective optimizations on general Riemannianmanifolds (without curvature constraints). Under the assumption of the localconvexity/quasi-convexity, local/global convergence results are established. Onthe other hand, without the assumption of the local convexity/quasi-convexity,but under a Kurdyka-{\L}ojasiewicz-like condition, local/global linearconvergence results are presented, which seem new even in Euclidean spacessetting and improve sharply the corresponding results in [24] in the case whenthe multiobjective optimization is reduced to the scalar case. Finally, for thespecial case when the inexact descent algorithm employing Armijo rule, ourresults improve sharply/extend the corresponding ones in [3,2,38].

Convergence analysis of inexact descent algorithm for multiobjective optimizations on Riemannian manifolds without curvature constraints