# A Derandomized Algorithm for RP-ADMM with Symmetric Gauss-Seidel Method

## TL;DR

This paper introduces a derandomized algorithm for multi-block RP-ADMM using symmetric Gauss-Seidel updates, achieving fast convergence for decomposable optimization problems.

## Contribution

It proposes a novel derandomized multi-block RP-ADMM algorithm with symmetric Gauss-Seidel iteration and establishes its linear convergence rate.

## Key findings

- Converges quickly with symmetric Gauss-Seidel iteration.
- Linear convergence rate for linear systems.
- Effective for multi-block decomposable problems.

## Abstract

For multi-block alternating direction method of multipliers(ADMM), where the objective function can be decomposed into multiple block components, we show that with block symmetric Gauss-Seidel iteration, the algorithm will converge quickly. The method will apply a block symmetric Gauss-Seidel iteration in the primal update and a linear correction that can be derived in view of Richard iteration. We also establish the linear convergence rate for linear systems.