Alternating proximal algorithms for linearly constrained variational inequalities: Application to domain decomposition for PDE’s

Abstract: Let be real Hilbert spaces, let , be closed convex functions and let , be linear continuous operators. Let us consider the constrained minimization problem Given a sequence which tends toward as , we study the following alternating proximal algorithm where and are positive parameters. It is shown that if the sequence tends moderately slowly toward , then the iterates of weakly converge toward a solution of . The study is extended to the setting of maximal monotone operators, for which a general ergodic convergence result is obtained. Applications are given in the area of domain decomposition for PDE’s. [Copyright &y& Elsevier]