REVIEW 1 cited by
A continuous perspective on the inertial corrected primal-dual proximal splitting
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
A continuous perspective on the inertial corrected primal-dual proximal splitting
read the original abstract
We give a continuous perspective on the Inertial Corrected Primal-Dual Proximal Splitting (IC-PDPS) proposed by Valkonen ({\it SIAM J. Optim.}, 30(2): 1391--1420, 2020) for solving saddle-point problems. The algorithm possesses nonergodic convergence rate and admits a tight preconditioned proximal point formulation which involves both inertia and additional correction. Based on new understandings on the relation between the discrete step size and rescaling effect, we rebuild IC-PDPS as a semi-implicit Euler scheme with respect to its iterative sequences and integrated parameters. This leads to two novel second-order ordinary differential equation (ODE) models that are equivalent under proper time transformation, and also provides an alternative interpretation from the continuous point of view. Besides, we present the convergence analysis of the Lagrangian gap along the continuous trajectory by using proper Lyapunov functions.
Forward citations
Cited by 1 Pith paper
-
Nesterov acceleration for strongly convex-strongly concave bilinear saddle point problems: discrete and continuous-time approaches
A Nesterov-accelerated primal-dual gradient algorithm and its continuous-time analogue achieve O((1 - min{sqrt(mu_F/L_F), sqrt(mu_G/L_G)})^k) convergence for strongly convex-strongly concave bilinear saddle point problems.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.