A proximal method for maximal monotone operators via discretization of a first order dissipative dynamical system

Abstract : We present an iterative method for finding zeroes of maximal monotone operators in a real Hilbert space. The underlying idea relies upon the discretization of a first order dissipative dynamical system which allows us to preserve the local feature, as well as to obtain convergence results. The main theorems do not only recover known convergence results of standard and inertial proximal methods, but also provide a theoretical basis for the application of new iterative methods.
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https://hal.univ-antilles.fr/hal-00780210
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Submitted on : Wednesday, January 23, 2013 - 3:05:37 PM
Last modification on : Wednesday, July 18, 2018 - 8:11:26 PM

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  • HAL Id : hal-00780210, version 1

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Paul-Emile Maingé, Abdellatif Moudafi. A proximal method for maximal monotone operators via discretization of a first order dissipative dynamical system. Journal of Convex Analysis, Heldermann, 2007, 14 (4), pp.869-878. ⟨hal-00780210⟩

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