Geodesic
Approximating Curves for Nonexpansive and Monotone Operators
Journal of convex analysis, Tome 13 (2006) no. 3, pp. 633-646

Voir la notice de l'article provenant de la source Heldermann Verlag

A classical tool in nonlinear analysis is the notion of an approximating curve, whereby a particular solution to a nonuniquely solvable problem is obtained as the limit of the solutions to uniquely solvable perturbed problems. We introduce and analyze new types of approximating curves for nonexpansive fixed point problems and monotone inclusion problems in Hilbert spaces. The solution attained by these curves solves a strictly monotone variational inequality over the original solution set. Various special cases are discussed.
Mots-clés : Approximating curve, monotone operator, nonexpansive operator, Tikhonov regularization, viscosity solution, variational inequality 
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     author = {P. L. Combettes and S. A. Hirstoaga},
     title = {Approximating {Curves} for {Nonexpansive} and {Monotone} {Operators}},
     journal = {Journal of convex analysis},
     pages = {633--646},
     publisher = {mathdoc},
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     number = {3},
     year = {2006},
     url = {http://geodesic.mathdoc.fr/item/JCA_2006_13_3_JCA_2006_13_3_a9/}
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P. L. Combettes; S. A. Hirstoaga. Approximating Curves for Nonexpansive and Monotone Operators. Journal of convex analysis, Tome 13 (2006) no. 3, pp. 633-646. http://geodesic.mathdoc.fr/item/JCA_2006_13_3_JCA_2006_13_3_a9/