# Random multi-block ADMM: an ALM based view for the QP case

arXiv: https://arxiv.org/abs/2012.09230 · HTML: https://mlsanity.com/paper/2012.09230/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Dec 2020.

## Built on by (most cited first, 1 of 1)

- [Training very large scale nonlinear SVMs using Alternating Direction Method of Multipliers coupled with the Hierarchically Semi-Separable kernel approximations](https://mlsanity.com/paper/2108.04167/) (2021)

## Abstract (arXiv)

Embedding randomization procedures in the Alternating Direction Method of Multipliers (ADMM) has recently attracted an increasing amount of interest as a remedy to the fact that the direct multi-block generalization of ADMM is not necessarily convergent. Even if, in practice, the introduction of such techniques could textitmitigate the diverging behaviour of the multi-block extension of ADMM, from the theoretical point of view, it can ensure just the textitconvergence in expectation, which may not be a good indicator of its robustness and efficiency. In this work, analysing the strongly convex quadratic programming case, we interpret the block Gauss-Seidel sweep performed by the multi-block ADMM in the context of the inexact Augmented Lagrangian Method. Using the proposed analysis, we are able to outline an alternative technique to those present in literature which, supported from stronger theoretical guarantees, is able to ensure the convergence of the multi-block generalization of the ADMM method.