- Strong asymptotic convergence of evolution equations governed by maximal monotone operators R Cominetti (rcominetdim.uchile.cl) J Peypouquet (juan.peypouquetusm.cl) S Sorin (sorinmath.jussieu.fr) Abstract: We consider the Tikhonov-like dynamics $-\dot u(t)\in A(u(t))+\varepsilon(t)u(t)$ where $A$ is a maximal monotone operator and the parameter function $\eps(t)$ tends to 0 for $t\to\infty$ with $\int_0^\infty\eps(t)dt=\infty$. 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 $\eps(t)$ has bounded variation, and provide a counterexample when this property fails. Keywords: Monotone operators, evolution equations, Tikhonov regularization Category 1: Applications -- Science and Engineering Category 2: Convex and Nonsmooth Optimization Citation: Journal of Differential Equations, Vol 245 (2008), 3753-3763. Download: Entry Submitted: 05/13/2008Entry Accepted: 05/13/2008Entry Last Modified: 01/21/2009Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Programming Society and by the Optimization Technology Center.