Convex Minimization over the Fixed Point Set of Demicontractive Mappings |
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Authors: | Paul-Emile Maingé |
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Affiliation: | (1) Département Scientifique Interfacultaire, GRIMAAG, Université des Antilles-Guyane, Campus de Schoelcher, 97230 Cedex, Martinique (F.W.I.) |
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Abstract: | This paper deals with a viscosity iteration method, in a real Hilbert space , for minimizing a convex function over the fixed point set of , a mapping in the class of demicontractive operators, including the classes of quasi-nonexpansive and strictly pseudocontractive operators. The considered algorithm is written as: x n+1 := (1 − w) v n + w T v n , v n := x n − α n Θ′(x n ), where w ∈ (0,1) and , Θ′ is the Gateaux derivative of Θ. Under classical conditions on T, Θ, Θ′ and the parameters, we prove that the sequence (x n ) generated, with an arbitrary , by this scheme converges strongly to some element in Argmin Fix(T) Θ. |
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Keywords: | 90C25 49M45 65C25 |
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