Solving nonsmooth inclusions in the convex case

The authors give a method for solving the inclusion 0∈F(x), where F is a set-valued map from a Hilbert space into a Banach space, whose graph is a closed convex set. The given algorithms are convergent if the problem is consistent and terminate after a finite number of iterations if otherwise. A convergence rate of geometrical progression is also obtained if a regularity condition of the Robinson’s type is assumed.