Convergence of inertial dynamics and proximal algorithms governed by maximally monotone operators

Hedy Attouch*, Juan Peypouquet

*Bijbehorende auteur voor dit werk

OnderzoeksoutputAcademicpeer review

18 Citaten (Scopus)

Samenvatting

We study the behavior of the trajectories of a second-order differential equation with vanishing damping, governed by the Yosida regularization of a maximally monotone operator with time-varying index, along with a new Regularized Inertial Proximal Algorithm obtained by means of a convenient finite-difference discretization. These systems are the counterpart to accelerated forward–backward algorithms in the context of maximally monotone operators. A proper tuning of the parameters allows us to prove the weak convergence of the trajectories to zeroes of the operator. Moreover, it is possible to estimate the rate at which the speed and acceleration vanish. We also study the effect of perturbations or computational errors that leave the convergence properties unchanged. We also analyze a growth condition under which strong convergence can be guaranteed. A simple example shows the criticality of the assumptions on the Yosida approximation parameter, and allows us to illustrate the behavior of these systems compared with some of their close relatives.

Originele taal-2English
Pagina's (van-tot)391-432
Aantal pagina's42
TijdschriftMathematical Programming
Volume174
Nummer van het tijdschrift1-2
DOI's
StatusPublished - 1-mrt-2019
Extern gepubliceerdJa

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