Éditeur(s) : HAL CCSDElsevier Résumé : International audience A forward-backward inertial procedure for solving the problem of finding a zero of the sum of two maximal monotone operators is proposed and its convergence is established under a cocoercivity condition with respect to the solution set. ISSN: 0377-0427
Éditeur(s) : HAL CCSDHeldermann Résumé : International audience 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. Journal of Convex Analysis
Éditeur(s) : HAL CCSDSpringer Résumé : International audience It is known that a locally Lipschitz function f is approximately convex if, and only if, its Clarke subdifferential ∂C f is a submonotone operator. The main object of this work is to extend the above characterization to the class of lower semicontinuous functions. To this end, we establish a new approximate mean value inequality involving three points. We also show that an analogue of the Rockafellar maximal monotonicity theorem holds for this class of functions and we discuss the case of arbitrary subdifferentials Mathematical Programming B
Éditeur(s) : HAL CCSD Résumé : International audience In this note we show that the splitting scheme of Passty [13] as well as the barycentric-proximal method of Lehdili & Lemaire [8] can be used to approximate a zero of the extended sum of maximal monotone operators. When the extended sum is maximal monotone, we generalize a convergence result obtained by Lehdili & Lemaire for convex functions to the case of maximal monotone operators. Moreover, we recover the main convergence results of Passty and Lehdili & Lemaire when the pointwise sum of the involved operators in maximal monotone. Studies in Computational Mathematics
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