Visco-penalization of the sum of two monotone operators
Hirstoaga, Sever A.; Combettes, Patrick L. (2008), Visco-penalization of the sum of two monotone operators, Nonlinear Analysis: Theory, Methods & Applications, 69, 2, p. 579-591. http://dx.doi.org/10.1016/j.na.2007.06.003
TypeArticle accepté pour publication ou publié
External document linkhttp://hal.archives-ouvertes.fr/hal-00619389/fr/
Journal nameNonlinear Analysis: Theory, Methods & Applications
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Abstract (EN)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.
Subjects / KeywordsYosida approximation; Viscosity; Variational inequality; Penalization; Monotone operator; Approximating curve
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