Staircase Parameterization in Dynamical Selection |
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Authors: | B Lemaire |
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Institution: | (1) Mathématiques, Université de Montpellier II, Place E. Bataillon, 34095 Montpellier Cedex 5, France |
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Abstract: | This paper deals with a variant of a dynamical selection scheme introduced by Attouch and Cominetti for ill-posed convex minimization which combines approximation with the steepest descent method by mean of a suitable parameterization of the approximation parameter as a function of the time. This variant applies to a general inclusion with a maximal monotone operator by mean of a staircase parameterization. A discrete analogue is also considered. Applications to selecting a particular zero of a maximal monotone operator or a particular fixed point of a nonexpansive mapping via regularization techniques are presented. Finally, the alternative use of well-posedness by perturbations is discussed. |
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Keywords: | approximation asymptotic control dynamical system fixed point iteration monotone nonexpansive regularization variational inequality well-posedness |
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