  In this paper, we propose an inertial forward backward splitting algorithm to
compute a zero of the sum of two monotone operators, with one of the two
operators being co-coercive. The algorithm is inspired by the accelerated
gradient method of Nesterov, but can be applied to a much larger class of
problems including convex-concave saddle point problems and general monotone
inclusions. We prove convergence of the algorithm in a Hilbert space setting
and show that several recently proposed first-order methods can be obtained as
special cases of the general algorithm. Numerical results show that the
proposed algorithm converges faster than existing methods, while keeping the
computational cost of each iteration basically unchanged.
