Abstract

We consider the Tikhonov-like dynamics - over(u, ̇) (t) ∈ A (u (t)) + ε (t) u (t) where A is a maximal monotone operator on a Hilbert space and the parameter function ε (t) tends to 0 as t → ∞ with ∫0 ∞ ε (t) d t = ∞. When A is the subdifferential of a closed proper convex function f, we establish strong convergence of u (t) towards the least-norm minimizer of f. In the general case we prove strong convergence towards the least-norm point in A-1 (0) provided that the function ε (t) has bounded variation, and provide a counterexample when this property fails. © 2008 Elsevier Inc. All rights reserved.