Hybrid steepest-descent methods for systems of variational inequalities with constraints of variational inclusions and convex minimization problems

Two hybrid steepest-descent schemes (implicit and explicit) for finding a solution of the general system of variational inequalities (in short, GSVI) with the constraints of finitely many variational inclusions for maximal monotone and inverse- strongly monotone mappings and a minimization problem for a convex and continuously Frechet differentiable functional (in short, CMP) have been presented in a real Hilbert space. We establish the strong convergence of these two hybrid steepest- descent schemes to the same solution of the GSVI, which is also a common solution of these finitely many variational inclusions and the CMP. Our results extend, improve, complement and develop the corresponding ones given by some authors recently in this area. Qc 2017 all rights reserved.