Convergence of the Proximal Point Method for Metrically Regular Mappings
نویسندگان
چکیده
منابع مشابه
Convergence of the Proximal Point Method for Metrically Regular Mappings
In this paper we consider the following general version of the proximal point algorithm for solving the inclusion T (x) 3 0, where T is a set-valued mapping acting from a Banach space X to a Banach space Y . First, choose any sequence of functions gn : X → Y with gn(0) = 0 that are Lipschitz continuous in a neighborhood of the origin. Then pick an initial guess x0 and find a sequence xn by appl...
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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 pr...
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In this paper, we use the concept of graph convergence of H(.,.)-co-accretive mapping introduced by [R. Ahmad, M. Akram, M. Dilshad, Graph convergence for the H(.,.)-co-accretive mapping with an application, Bull. Malays. Math. Sci. Soc., doi: 10.1007/s40840-014-0103-z, 2014$] and define an over-relaxed proximal point method to obtain the solution of a generalized variational inclusion problem ...
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ژورنال
عنوان ژورنال: ESAIM: Proceedings
سال: 2007
ISSN: 1270-900X
DOI: 10.1051/proc:071701