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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

Type
Article accepté pour publication ou publié
External document link
http://hal.archives-ouvertes.fr/hal-00619389/fr/
Date
2008
Journal name
Nonlinear Analysis: Theory, Methods & Applications
Volume
69
Number
2
Publisher
Elsevier
Pages
579-591
Publication identifier
Metadata
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Author(s)
Hirstoaga, Sever A.
Combettes, Patrick L.
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 / Keywords
Yosida approximation; Viscosity; Variational inequality; Penalization; Monotone operator; Approximating curve