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A bundle method using two polyhedral approximations of the $$\varepsilon $$ ε -enlargement of a maximal monotone operator

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  • Ludovic Nagesseur

    (LAMIA, Université des Antilles)

Abstract

Until now, a few bundle methods for general maximal monotone operators exist and they were only employed with one polyhedral approximation of the $$\varepsilon $$ ε -enlargement of the maximal monotone operator considered. However, we find in the literature several hybrid-proximal methods which could be adapted with a great deal of bundle techniques in order to find a zero of a maximal monotone operator; yet, we could also consider the use of two polyhedral approximations. The method developed in this study has used a double polyhedral approximation at each iteration. Besides, as an application, we give a bundle method for a forward–backward type algorithm.

Suggested Citation

  • Ludovic Nagesseur, 2016. "A bundle method using two polyhedral approximations of the $$\varepsilon $$ ε -enlargement of a maximal monotone operator," Computational Optimization and Applications, Springer, vol. 64(1), pages 75-100, May.
    • Handle: RePEc:spr:coopap:v:64:y:2016:i:1:d:10.1007_s10589-015-9808-7
    DOI: 10.1007/s10589-015-9808-7
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    References listed on IDEAS

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    1. Regina S. Burachik & Alfredo N. Iusem, 2008. "Set-Valued Mappings and Enlargements of Monotone Operators," Springer Optimization and Its Applications, Springer, number 978-0-387-69757-4, September.
    2. Regina S. Burachik & Alfredo N. Iusem, 2008. "Enlargements of Monotone Operators," Springer Optimization and Its Applications, in: Set-Valued Mappings and Enlargements of Monotone Operators, chapter 0, pages 161-220, Springer.
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