An improved self-adaptive Tseng-type method for solving variational inclusion problems on Hadamard manifolds.

In this paper we propose an inertial Tseng-type splitting method for solving variational inclusion problems in the setting of an Hadamard manifold. Most of the proposed splitting methods in the literature require one of the operators to be co-coercive, or monotone and Lipschitz continuous. Using our proposed method, we establish a convergence result regarding an algorithm for solving variational inclusion problems under the assumption that one of our operators is monotone and uniformly continuous. We also present some numerical examples to demonstrate the performance of our iterative algorithm in comparison with some related methods in the literature. Many already studied related problems in the literature can be considered special cases of the problem we tackle in the present manuscript.