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| HAL: hal-00619389, version 1 |
| DOI: 10.1016/j.na.2007.06.003 |
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| Nonlinear Analysis: Theory, Methods and Applications 69, 2 (2008) 579-591 |
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| Visco-penalization of the sum of two monotone operators |
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| Patrick Louis Combettes 1Sever Adrian Hirstoaga 2 |
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| (2008-07-15) |
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| A new type of approximating curve for finding a particular zero of the sum of two maximal monotone operators in a Hilbert space is investigated. This curve consists of the zeros of perturbed problems in which one operator is replaced with its Yosida approximation and a viscosity term is added. As the perturbation vanishes, the curve is shown to converge to the zero of the sum that solves a particular strictly monotone variational inequality. As an off-spring of this result, we obtain an approximating curve for finding a particular zero of the sum of several maximal monotone operators. Applications to convex optimization are discussed. |
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| 1: | Laboratoire Jacques-Louis Lions (LJLL) |
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CNRS : UMR7598 – Université Pierre et Marie Curie [UPMC] - Paris VI |
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| 2: | CEntre de REcherches en MAthématiques de la DEcision (CEREMADE) |
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CNRS : UMR7534 – Université Paris IX - Paris Dauphine |
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| Subject | : | Mathematics/Functional Analysis Mathematics/Optimization and Control |
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| Approximating curve – Monotone operator – Penalization – Variational inequality – Viscosity – Yosida approximation |
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| hal-00619389, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00619389 | |
| oai:hal.archives-ouvertes.fr:hal-00619389 | |
| From: Sever Adrian Hirstoaga | |
| Submitted on: Tuesday, 6 September 2011 11:41:05 | |
| Updated on: Tuesday, 6 September 2011 11:57:47 | |
