Convergence analysis of inexact proximal point algorithms on Hadamard manifolds

Abstract

Inexact proximal point methods are extended to find singular points for multivalued vector fields on Hadamard manifolds. Convergence criteria are established under some mild conditions. In particular, in the case of proximal point algorithm, that is, $$\varepsilon _n=0$$ ? n = 0 for each $$n$$ n , our results improve sharply the corresponding results in Li et al. (2009). Applications to optimization problems, variational inequality problems and gradient methods are also given.