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<identifier>oai:HAL:hal-00776638v1</identifier>
<datestamp>2017-12-21</datestamp>
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<setSpec>subject:math</setSpec>
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<setSpec>collection:UNIV-AG</setSpec>
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<setSpec>collection:CEREGMIA</setSpec>
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<metadata><dc>
<publisher>HAL CCSD</publisher>
<title lang=en>A relaxed alternating CQ-algorithm for convex feasibility</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-00776638</identifier>
<identifier>https://hal.univ-antilles.fr/hal-00776638</identifier>
<source>https://hal.univ-antilles.fr/hal-00776638</source>
<source>Nonlinear Analysis: Theory, Methods and Applications, Elsevier, 2013, 79, pp.117-121. 〈10.1016/j.na.2012.11.013〉</source>
<identifier>DOI : 10.1016/j.na.2012.11.013</identifier>
<relation>info:eu-repo/semantics/altIdentifier/doi/10.1016/j.na.2012.11.013</relation>
<language>en</language>
<subject lang=en>Feasibility problem</subject>
<subject lang=en>CQ-algorithm</subject>
<subject lang=en>Alternating algorithm</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>Let H1,H2,H3 be real Hilbert spaces, let C⊂H1, Q⊂H2 be two nonempty closed convex level sets, let A:H1→H3, B:H2→H3 be two bounded linear operators. Our interest is in solving the following new convex feasibility problem Find x∈C,y∈Q such that Ax=By, which allows asymmetric and partial relations between the variables x and y. In this paper, we present and study the convergence of a relaxed alternating CQ-algorithm (RACQA) and show that the sequences generated by such an algorithm weakly converge to a solution of (1.1). The interest of RACQA is that we just need projections onto half-spaces, thus making the relaxed CQ-algorithm implementable. Note that, by taking B=I, in (1.1), we recover the split convex feasibility problem originally introduced in Censor and Elfving (1994) [13] and used later in intensity-modulated radiation therapy (Censor et al. (2006) [11]). We also recover the relaxed CQ-algorithm introduced by Yang (2004) [8] by particularizing both B and a given parameter.</description>
<date>2013-03</date>
</dc>
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