Visco-penalization of the sum of two monotone operators

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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Nonlinear Analysis: Theory, Methods and Applications, Elsevier, 2008, 69 (2), pp.579-591. 〈10.1016/j.na.2007.06.003〉
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Patrick Louis Combettes, Sever Adrian Hirstoaga. Visco-penalization of the sum of two monotone operators. Nonlinear Analysis: Theory, Methods and Applications, Elsevier, 2008, 69 (2), pp.579-591. 〈10.1016/j.na.2007.06.003〉. 〈hal-00619389〉

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