Abstract
We consider the Tikhonov-like dynamics − 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.
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