Ergodic convergence to a zero of the extended sum of two maximal monotone operators
Moudafi, Abdellatif ; Théra, Michel
HAL, hal-00778164 / Harvested from HAL
Text on HAL
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.
Publié le : 2001-12-31
Classification:  [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] 
@article{hal-00778164,
     author = {Moudafi, Abdellatif and Th\'era, Michel},
     title = {Ergodic convergence to a zero of the extended sum of two maximal monotone operators},
     journal = {HAL},
     volume = {2001},
     number = {0},
     year = {2001},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00778164}
}

Moudafi, Abdellatif; Théra, Michel. Ergodic convergence to a zero of the extended sum of two maximal monotone operators. HAL, Tome 2001 (2001) no. 0, . http://gdmltest.u-ga.fr/item/hal-00778164/