In this work we analyze a first order method especially tailored for smooth saddle point problems, based on an alternating extragradient scheme. The proposed method is based on three successive projection steps, which can be computed also with respect to non Euclidean metrics. The stepsize...

The concept of pseudomonotone vector field on Hadamard manifold is introduced. A variant of Korpelevich’s method for solving the variational inequality problem is extended from Euclidean spaces to constant curvature Hadamard manifolds. Under a pseudomonotone assumption on the underlying vector...

In this paper, we give a short and simple proof of the recent result of Ceng et al. (Math Methods Oper Res 67(3):375–390, <CitationRef CitationID="CR1">2008</CitationRef>). Copyright Springer-Verlag 2011