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Backward Penalty Schemes for Monotone Inclusion Problems

Author

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  • Sebastian Banert

    (University of Vienna)

  • Radu Ioan Boţ

    (University of Vienna)

Abstract

In this paper, we are concerned with solving monotone inclusion problems expressed by the sum of a set-valued maximally monotone operator with a single-valued maximally monotone one and the normal cone to the nonempty set of zeros of another set-valued maximally monotone operator. Depending on the nature of the single-valued operator, we propose two iterative penalty schemes, both addressing the set-valued operators via backward steps. The single-valued operator is evaluated via a single forward step if it is cocoercive, and via two forward steps if it is monotone and Lipschitz continuous. The latter situation represents the starting point for dealing with complexly structured monotone inclusion problems from algorithmic point of view.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:166:y:2015:i:3:d:10.1007_s10957-014-0700-x
    DOI: 10.1007/s10957-014-0700-x
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    References listed on IDEAS

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    1. 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.
    2. 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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    2. 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.

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