Extragradient method for monotone variational inequality in CAT(0) spaces

The problem of finding a solution to a variational inequality problem, which involves monotone mappings on certain CAT(0) spaces, is analyzed and solved by extending the well-known extragradient scheme to these spaces. For a monotone mapping, the sequence generated by the scheme is shown to converge to a solution of the problem. The ambient spaces provide tools that allow non-convex (or constrained) problems in Euclidean spaces to be translated into geodesic convex (or unconstrained) problems. To illustrate the proposed approach and the scheme’s implementation, examples are provided.