untitled
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<identifier>oai:HAL:hal-00778175v1</identifier>
<datestamp>2017-12-21</datestamp>
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<setSpec>subject:math</setSpec>
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<setSpec>collection:CEREGMIA</setSpec>
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<metadata><dc>
<publisher>HAL CCSD</publisher>
<title lang=en>A proximal iterative approach to a non-convex optimization problem</title>
<creator>Moudafi, Abdellatif</creator>
<contributor>Centre de Recherche en Economie, Gestion, Modélisation et Informatique Appliquée (CEREGMIA) ; Université des Antilles et de la Guyane (UAG)</contributor>
<description>International audience</description>
<source>ISSN: 0362-546X</source>
<source>Nonlinear Analysis: Theory, Methods and Applications</source>
<publisher>Elsevier</publisher>
<identifier>hal-00778175</identifier>
<identifier>https://hal.univ-antilles.fr/hal-00778175</identifier>
<source>https://hal.univ-antilles.fr/hal-00778175</source>
<source>Nonlinear Analysis: Theory, Methods and Applications, Elsevier, 2010, 72 (2), pp.704-709. 〈10.1016/j.na.2009.07.011〉</source>
<identifier>DOI : 10.1016/j.na.2009.07.011</identifier>
<relation>info:eu-repo/semantics/altIdentifier/doi/10.1016/j.na.2009.07.011</relation>
<language>en</language>
<subject lang=en>Optimization</subject>
<subject lang=en>Prox-regularity</subject>
<subject lang=en>Krasnosel'skii-Mann algorithm</subject>
<subject lang=en>Fixed-point</subject>
<subject>[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]</subject>
<type>info:eu-repo/semantics/article</type>
<type>Journal articles</type>
<description lang=en>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.</description>
<date>2010-01-15</date>
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