untitled
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<datestamp>2017-12-21</datestamp>
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<publisher>HAL CCSD</publisher>
<title lang=es>Proximal point algorithm extended to equilibrium problems</title>
<creator>Moudafi, Abdellatif</creator>
<contributor>Département de Mathématiques et Informatique (D.M.I.) ; Université des Antilles et de la Guyane (UAG) - Université des Antilles (Pôle Guadeloupe) ; Université des Antilles (UA) - Université des Antilles (UA)</contributor>
<description>International audience</description>
<source>Journal of Natural Geometry</source>
<identifier>hal-00773194</identifier>
<identifier>https://hal.univ-antilles.fr/hal-00773194</identifier>
<source>https://hal.univ-antilles.fr/hal-00773194</source>
<source>Journal of Natural Geometry, 1999, 15 (1-2), pp.91-100</source>
<language>en</language>
<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>The author proposes a generalized proximal method for solving an equilibrium problem which consists in finding x 2 K such that F(x, y) 0, for all y 2 K, where K is a nonempty, convex and closed set of a real Hilbert space X, and F:K ×K !Ris a given bifunction with F(x, x) = 0 for all x 2 K. The weak convergence of the sequence generated by the method is proved under the assumptions of monotonicity and convexity, with respect to the second argument y (for every fixed x 2 K), of the bifunction F. Replacing the assumption of monotonicity with the one of strong monotonicity on F, a strong convergence result is obtained. A second strong convergence theorem is proved under the hypotheses of monotonicity and a new assumption of "co-Lipschitz continuity at 0" of the operator F. Applications to convex optimization, to the problem of finding a zero of a maximal monotone operator and to Nash equilibria problems are provided.</description>
<date>1999-10-28</date>
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