On the (linear) convergence of Generalized Newton Inexact ADMM

TMLR Paper5874 Authors

Abstract:

This paper presents GeNI-ADMM, a framework for large-scale composite convex optimiza-
tion that facilitates theoretical analysis of both existing and new approximate ADMM
schemes. GeNI-ADMM encompasses any ADMM algorithm that solves a first- or second-
order approximation to the ADMM subproblem inexactly. GeNI-ADMM exhibits the usual
O(1/t)-convergence rate under standard hypotheses and converges linearly under additional
hypotheses such as strong convexity. Further, the GeNI-ADMM framework provides explicit
convergence rates for ADMM variants accelerated with randomized linear algebra, such as
NysADMM and sketch-and-solve ADMM, resolving an important open question on the con-
vergence of these methods. This analysis quantifies the benefit of improved approximations
and can aid in the design of new ADMM variants with faster convergence

Submission Length: Long submission (more than 12 pages of main content)

Previous TMLR Submission Url: https://openreview.net/forum?id=ofAXexUGLO&referrer=%5BAuthor%20Console%5D(%2Fgroup%3Fid%3DTMLR%2FAuthors%23your-submissions)

Changes Since Last Submission: Fixed the issue where the header saying "under review as a submission to TMLR" was missing, which resulted in rejection.

Assigned Action Editor: ~Ahmet_Alacaoglu2

Submission Number: 5874