Samenvatting
We establish the weak convergence of inertial Krasnoselskii-Mann iterations towards a common fixed point of a family of quasi-nonexpansive operators, along with estimates for the non-asymptotic rate at which the residuals vanish. Strong and linear convergence are obtained in the quasi-contractive setting. In both cases, we highlight the relationship with the non-inertial case, and show that passing from one regime to the other is a continuous process in terms of the hypotheses on the parameters. Numerical illustrations are provided for an inertial primal-dual method and an inertial three-operator splitting algorithm, whose performance is superior to that of their non-inertial counterparts.
Originele taal-2 | English |
---|---|
Artikelnummer | 10 |
Aantal pagina's | 27 |
Tijdschrift | Set-Valued and Variational Analysis |
Volume | 32 |
Nummer van het tijdschrift | 2 |
DOI's | |
Status | Published - 26-mrt.-2024 |