Forward–Backward Penalty Scheme for Constrained Convex Minimization Without Inf-Compactness

Nahla Noun () and Juan Peypouquet ()
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Nahla Noun: Université Montpellier 2
Juan Peypouquet: Universidad Técnica Federico Santa María

Journal of Optimization Theory and Applications, 2013, vol. 158, issue 3, No 8, 787-795

Abstract: 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.

Keywords: Constrained convex optimization; Forward–backward algorithms; Exterior penalization (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-013-0296-6

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