Visco-penalization of the sum of two monotone operators |
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Authors: | Patrick L Combettes Sever A Hirstoaga |
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Institution: | 1. Laboratoire Jacques-Louis Lions, Faculté de Mathématiques, Université Pierre et Marie Curie–Paris 6, 75005 Paris, France;2. CEREMADE, Université Paris-Dauphine, 75775 Paris, France |
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Abstract: | 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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Keywords: | Approximating curve Monotone operator Penalization Variational inequality Viscosity Yosida approximation |
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