Uniformity and inexact version of a proximal method for metrically regular mappings

[摘要] We study stability properties of a proximal point algorithm for solving the inclusion 0 is an element of 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 is an element of T(x). (C) 2007 Elsevier Inc. All rights reserved.

[发布日期] 2007-11-01

[关键词] proximal point algorithm;set-valued mapping;metric regularity;strong subregularity;strong regularity