A comparative numerical study of graph-based splitting algorithms for linear subspaces

TL;DR

This paper compares six graph-based splitting algorithms for linear subspaces through numerical experiments, identifying optimal parameters and analyzing iteration counts to inform future theoretical work.

Contribution

It provides a systematic numerical comparison of algorithms for linear subspaces, highlighting performance patterns and optimal parameters.

Findings

Identified best relaxation parameters for each algorithm.

Compared iteration counts to reach stopping criteria.

Provided numerical evidence to guide theoretical analysis.

Abstract

In this note, we test the performance of six algorithms from the family of graph-based splitting methods [SIAM J. Optim., 34 (2024), pp. 1569-1594] specialized to normal cones of linear subspaces. To do this, we first implement some numerical experiments to determine the best relaxation parameter for each algorithm. Then, we compare the number of iterations each algorithm requires to reach a given stopping criterion, using the previously identified best relaxation parameter. The numerical results allow us to identify some relevant patterns and provide numerical evidence that may guide further theoretical analysis.