Journal of Convex Analysis 13 (2006), No. 3, 633--646
Copyright Heldermann Verlag 2006
Approximating Curves for Nonexpansive and Monotone Operators
Patrick L. Combettes
Laboratoire Jacques-Louis Lions, Université P. et M. Curie / Paris 6, 75005 Paris, France
plc@math.jussieu.fr
Sever A. Hirstoaga
Laboratoire Jacques-Louis Lions, Université P. et M. Curie / Paris 6, 75005 Paris, France
hirstoag@ann.jussieu.fr
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.
Keywords: Approximating curve, monotone operator, nonexpansive operator, Tikhonov regularization, viscosity solution, variational inequality.
[ Fulltext-pdf (394 KB)] for subscribers only.