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Inclusions Monotones en Dualité et Applications

Abstract : The goal of this thesis is to develop new splitting techniques for set-valued operators to solve structured monotone inclusion problems in Hilbert spaces. Duality plays a central role in this work. It allows us to obtain decompositions which would not be available through a purely primal approach. We develop several fixed and variable metric algorithms in a unified framework, and show in particular that many existing methods are special cases of the forward-backward method formulated in a suitable product space. The proposed methods are applied to variational inequalities, minimization problems, inverse problems, signal processing problems, feasibility problems, and best approximation problems. Next, we introduce the notion of a variable metric quasi-Fejér sequence and analyze its asymptotic properties. These results allow us to obtain extensions of splitting schemes to problems in which the metric varies at each iteration.
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https://theses.hal.science/tel-00816116
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Submitted on : Friday, April 19, 2013 - 5:41:04 PM
Last modification on : Sunday, June 26, 2022 - 5:12:23 AM
Long-term archiving on: : Saturday, July 20, 2013 - 4:04:21 AM

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  • HAL Id : tel-00816116, version 1

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Bang Cong Vu. Inclusions Monotones en Dualité et Applications. Optimisation et contrôle [math.OC]. Université Pierre et Marie Curie - Paris VI, 2013. Français. ⟨NNT : ⟩. ⟨tel-00816116⟩

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