"Forward-backward penalty scheme for constrained convex minimization without inf-compactness”

Research areas:
Year:
2013
Type of Publication:
Article
Keywords:
Constrained convex optimization, Forward backward algorithms, Exterior penalization
Authors:
  • N Noun
  • J Peypouquet
Journal:
Journal of Optimization Theory and Applications
Volume:
158
Pages:
787-795
ISSN:
0022-3239
Abstract:
In order to solve constrained minimization problems, Attouch et al. propose a forward–backward 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.