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

Ludovic Nagesseur ()
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Ludovic Nagesseur: LAMIA, Université des Antilles

Computational Optimization and Applications, 2016, vol. 64, issue 1, No 3, 75-100

Abstract: 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.

Keywords: Maximal monotone operator; $$\varepsilon $$ ε -Enlargement; Proximal point algorithm; Splitting algorithms; Bundle methods (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10589-015-9808-7

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