A note on alternating direction method of multipliers with generalized augmented terms for constrained sparse least absolute deviation

TL;DR

This paper introduces an enhanced ADMM algorithm with generalized augmented terms and a residual balance technique, improving efficiency for constrained sparse least absolute deviation problems.

Contribution

It proposes a novel ADMM-GAT algorithm with a residual balance method tailored for constrained sparse least absolute deviation, extending previous work.

Findings

Enhanced convergence efficiency demonstrated

Effective handling of constrained sparse least absolute deviation

Algorithmic details for practical implementation

Abstract

This technical note is an ancillary material for our research paper (Itoh and Parente, 2019). We discuss an alternating direction method of multipliers with generalized augmented terms (ADMM-GAT) and introduce a generalized residual balance technique for efficiently employing ADMM-GAT. These techniques are applied to least absolute deviation and its constrained version and their algorithmic details are presented. These algorithms are used for the implementation of the method described in (Itoh and Parente, 2019).