Éditeur(s) :
HAL CCSD Elsevier Résumé : International audience
We consider a variable Krasnosel'skii-Mann algorithm for approximating critical points of a prox-regular function or equivalently for finding fixed-points of its proximal mapping proxλf. The novelty of our approach is that the latter is not non-expansive any longer. We prove that the sequence generated by such algorithm (via the formula xk+1=(1−αk)xk+αkproxλkfxk, where (αk) is a sequence in (0,1)), is an approximate fixed-point of the proximal mapping and converges provided that the function under consideration satisfies a local metric regularity condition.
ISSN: 0362-546X
hal-00778175
https://hal.univ-antilles.fr/hal-00778175 DOI : 10.1016/j.na.2009.07.011