Inexact proximal point algorithms for inclusion problems on hadamard manifolds

This paper proposes inexact proximal point algorithms for computing the zeros of sum of two set-valued vector fields on Hadamard manifolds. The convergence results of the proposed algorithm are established under the assump-tion that the one set-valued vector field is monotone and lower semicontinuous and another one is monotone and upper Kuratowski semicontinuous. An example is given to illustrate the proposed algorithms and convergence results. As an application of the proposed algorithms and convergence results, an algorithm and its convergence result are derived for solving set-valued variational inequality problems in the setting of Hadamard manifolds.