Optimization Online


Strong asymptotic convergence of evolution equations governed by maximal monotone operators

R Cominetti (rcominet***at***dim.uchile.cl)
J Peypouquet (juan.peypouquet***at***usm.cl)
S Sorin (sorin***at***math.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.


Entry Submitted: 05/13/2008
Entry Accepted: 05/13/2008
Entry Last Modified: 01/21/2009

Modify/Update this entry

  Visitors Authors More about us Links
  Subscribe, Unsubscribe
Digest Archive
Search, Browse the Repository


Coordinator's Board
Classification Scheme
Give us feedback
Optimization Journals, Sites, Societies
Mathematical Programming Society