Aragón Artacho, Francisco Javier, Geoffroy, Michel H.
Uniformity and inexact version of a proximal method for metrically regular mappings
ARAGÓN ARTACHO, Francisco Javier; GEOFFROY, Michel H. "Uniformity and inexact version of a proximal method for metrically regular mappings". Journal of Mathematical Analysis and Applications. Vol. 335, Issue 1 (1 Nov. 2007). ISSN 0022-247X, pp. 168-183
URI: http://hdl.handle.net/10045/8060
DOI: 10.1016/j.jmaa.2007.01.050
ISSN: 0022-247X
Abstract: 
We study stability properties of a proximal point algorithm for solving the inclusion 0 ∈ T (x) when T
is a set-valued mapping that is not necessarily monotone. More precisely we show that the convergence of
our algorithm is uniform, in the sense that it is stable under small perturbations whenever the set-valued
mapping T is metrically regular at a given solution. We present also an inexact proximal point method for
strongly metrically subregular mappings and show that it is super-linearly convergent to a solution to the
inclusion 0 ∈ T (x).
Keywords:Proximal point algorithm, Set-valued mapping, Metric regularity, Strong subregularity, Strong regularity
Elsevier
info:eu-repo/semantics/article