Convergence of proximal solutions for evolution inclusions with time-dependent maximal monotone operators - Équipe Méthodes et Algorithmes en Commande Accéder directement au contenu
Article Dans Une Revue Mathematical Programming, Series A Année : 2021

Convergence of proximal solutions for evolution inclusions with time-dependent maximal monotone operators

Résumé

This article studies the solutions of time-dependent differential inclusions which is motivated by their utility in the modeling of certain physical systems. The differential inclusion is described by a time-dependent set-valued mapping having the property that, for a given time instant, the set-valued mapping describes a maximal monotone operator. By successive application of a proximal operator, we construct a sequence of functions parameterized by the sampling time that corresponds to the discretization of the continuous-time system. Under certain mild assumptions on the regularity with respect to the time argument, and using appropriate tools from functional and variational analysis, this sequence is then shown to converge to the unique solution of the original differential inclusion. The result is applied to develop conditions for well-posedness of differential equations interconnected with nonsmooth time-dependent complementarity relations, using passivity of underlying dynamics (equivalently expressed in terms of linear matrix inequalities).
Fichier principal
Vignette du fichier
convProxMathProg2021.pdf (605.95 Ko) Télécharger le fichier
Origine : Fichiers éditeurs autorisés sur une archive ouverte

Dates et versions

hal-02144478 , version 1 (30-05-2019)
hal-02144478 , version 2 (02-07-2021)

Identifiants

Citer

M Kanat Camlibel, Luigi Iannelli, Aneel Tanwani. Convergence of proximal solutions for evolution inclusions with time-dependent maximal monotone operators. Mathematical Programming, Series A, 2021, ⟨10.1007/s10107-021-01666-7⟩. ⟨hal-02144478v2⟩
296 Consultations
217 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More