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.
Original language | English |
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Pages (from-to) | 3753-3763 |
Number of pages | 11 |
Journal | Journal of Differential Equations |
Volume | 245 |
Issue number | 12 |
DOIs | |
State | Published - 15 Dec 2008 |
Keywords
- Maximal monotone operators
- Tikhonov regularization