A Regularized Hybrid Steepest Descent Method for Variational Inclusions

Abstract : This article is concerned with a generalization of the hybrid steepest descent method from variational inequalities to the multivalued case. This will be reached by replacing the multivalued operator by its Yosida approximate, which is always Lipschitz continuous. It is worth mentioning that the hybrid steepest descent method is an algorithmic solution to variational inequality problems over the fixed point set of certain nonexpansive mappings and has remarkable applicability to the constrained nonlinear inverse problems like image recovery and MIMO communication systems
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https://hal.univ-antilles.fr/hal-00776641
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Submitted on : Tuesday, January 15, 2013 - 8:26:30 PM
Last modification on : Wednesday, July 18, 2018 - 8:11:27 PM

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Abdellatif Moudafi. A Regularized Hybrid Steepest Descent Method for Variational Inclusions. Numerical Functional Analysis and Optimization, Taylor & Francis, 2012, 33 (1), pp.39-47. ⟨10.1080/01630563.2011.619676⟩. ⟨hal-00776641⟩

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