Uniformity and inexact version of a proximal method for metrically regular mappings |
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Authors: | Francisco J Aragón Artacho Michel H Geoffroy |
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Institution: | a Department of Statistics and Operations Research, University of Alicante, 03071 Alicante, Spain b Laboratoire AOC, Departement de Mathématiques, Université Antilles-Guyane, F-97159 Pointe-à-Pitre, Guadeloupe |
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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). |
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Keywords: | Proximal point algorithm Set-valued mapping Metric regularity Strong subregularity Strong regularity |
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