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Stratégies multicouche, avec mémoire, et à métrique variable en méthodes de point fixe pour l'éclatement d'opérateurs monotones et l'optimisation

Abstract : Several apparently unrelated strategies coexist to implement algorithms for solving monotone inclusions in Hilbert spaces. We propose a synthetic framework for fixed point construction which makes it possible to capture various algorithmic approaches, clarify and generalize their asymptotic behavior, and design new iterative schemes for nonlinear analysis and convex optimization. Our methodology, which is anchored on an averaged quasinonexpansive operator composition model, allows us to advance the theory of fixed point algorithms on several fronts, and to impact their application fields. Numerical examples are provided in the context of image restoration, where we propose a new viewpoint on the formulation of variational problems.
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Submitted on : Wednesday, September 23, 2020 - 2:22:09 PM
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Lilian Glaudin. Stratégies multicouche, avec mémoire, et à métrique variable en méthodes de point fixe pour l'éclatement d'opérateurs monotones et l'optimisation. Analyse numérique [math.NA]. Sorbonne Université, 2019. Français. ⟨NNT : 2019SORUS119⟩. ⟨tel-02946811⟩

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