ForwardBackward Penalty Scheme for Constrained Convex Minimization Without Inf-Compactness
In order to solve constrained minimization problems, Attouch et al. propose a forwardbackward algorithm that involves an exterior penalization scheme in the forward step. They prove that every sequence generated by the algorithm converges weakly to a solution of the minimization problem if either the objective function or the penalization function corresponding to the feasible set is inf-compact. Unfortunately, this assumption leaves out problems that are not coercive, as well as several interesting applications in infinite-dimensional spaces. The purpose of this short article is to show this convergence result without the inf-compactness assumption.
forwardbackward algorithms exterior penalization constrained convex optimization