Iterative Algorithms for System of Variational Inclusions in Hadamard Manifolds

In this paper, we consider system of variational inclusions and its several spacial cases, namely, alternating point problems, system of variational inequalities, etc., in the setting of Hadamard manifolds. We propose an iterative algorithm for solving system of variational inclusions and study its convergence analysis. Several special cases of the proposed algorithm and convergence result are also presented. We present application to constraints minimization problems for bifunctions in the setting of Hadamard manifolds. At the end, we illustrate proposed algorithms and convergence analysis by a numerical example. The algorithms and convergence results of this paper either improve or extend known algorithms and convergence results from linear structure to Hadamard manifolds.