A dynamical approach to convex minimization coupling approximation with the steepest descent method

H. Attouch, R. Cominetti

Resultado de la investigación: Contribución a una revistaArtículorevisión exhaustiva

93 Citas (Scopus)

Resumen

We study the asymptotic behavior of the solutions to evolution equations of the form 0 ∈u̇(t) + ∂f(u(t),ε(t)); u(0) = u0, where {f(·,ε):ε>0} is a family of strictly convex functions whose minimum is attained at a unique point x(ε). Assuming that x(ε) converges to a point x* as ε tends to 0, and depending on the behavior of the optimal trajectory x(ε), we derive sufficient conditions on the parametrization ε(t) which ensure that the solution u(t) of the evolution equation also converges to x* when t→ + ∞. The results are illustrated on three different penalty and viscosity-approximation methods for convex minimization.

Idioma originalInglés
Páginas (desde-hasta)519-540
Número de páginas22
PublicaciónJournal of Differential Equations
Volumen128
N.º2
DOI
EstadoPublicada - 1 jul. 1996

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