A Dynamical Approach to Convex Minimization Coupling Approximation with the Steepest Descent Method

✍ Scribed by H. Attouch; R. Cominetti

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 805 KB
• Volume: 128
• Category: Article
• ISSN: 0022-0396
• DOI: 10.1006/jdeq.1996.0104

✦ Synopsis

We study the asymptotic behavior of the solutions to evolution equations of the form 0 # u* (t)+ f(u(t), =(t)); u(0)=u 0 , where [ f( } , =): =>0] is a family of strictly convex functions whose minimum is attained at a unique point x(=). Assuming that x(=) converges to a point x* as = tends to 0, and depending on the behavior of the optimal trajectory x(=), we derive sufficient conditions on the parametrization =(t) which ensure that the solution u(t) of the evolution equation also converges to x* when t Ä + . The results are illustrated on three different penalty and viscosityapproximation methods for convex minimization.