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

Author

Listed:
  • Nahla Noun

    (Université Montpellier 2
    Faculté des Sciences 1 et Ecole Doctorale des Sciences et de Technologie)

  • Juan Peypouquet

    (Universidad Técnica Federico Santa María)

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.

Suggested Citation

  • Nahla Noun & Juan Peypouquet, 2013. "Forward–Backward Penalty Scheme for Constrained Convex Minimization Without Inf-Compactness," Journal of Optimization Theory and Applications, Springer, vol. 158(3), pages 787-795, September.
    • Handle: RePEc:spr:joptap:v:158:y:2013:i:3:d:10.1007_s10957-013-0296-6
    DOI: 10.1007/s10957-013-0296-6
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    References listed on IDEAS

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    1. Juan Peypouquet, 2012. "Coupling the Gradient Method with a General Exterior Penalization Scheme for Convex Minimization," Journal of Optimization Theory and Applications, Springer, vol. 153(1), pages 123-138, April.
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    Cited by:

    1. Sebastian Banert & Radu Ioan Boţ, 2015. "Backward Penalty Schemes for Monotone Inclusion Problems," Journal of Optimization Theory and Applications, Springer, vol. 166(3), pages 930-948, September.
    2. Nimit Nimana & Narin Petrot, 2019. "Generalized forward–backward splitting with penalization for monotone inclusion problems," Journal of Global Optimization, Springer, vol. 73(4), pages 825-847, April.

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    1. Sebastian Banert & Radu Ioan Boţ, 2015. "Backward Penalty Schemes for Monotone Inclusion Problems," Journal of Optimization Theory and Applications, Springer, vol. 166(3), pages 930-948, September.
    2. Nimit Nimana & Narin Petrot, 2019. "Generalized forward–backward splitting with penalization for monotone inclusion problems," Journal of Global Optimization, Springer, vol. 73(4), pages 825-847, April.

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