Improved Convergence Bounds For Operator Splitting Algorithms With Rare Extreme Errors
Optimization and Control
2023-07-06 v2 Signal Processing
Abstract
In this paper, we improve upon our previous work[24,22] and establish convergence bounds on the objective function values of approximate proximal-gradient descent (AxPGD), approximate accelerated proximal-gradient descent (AxAPGD) and approximate proximal ADMM (AxWLM-ADMM) schemes. We consider approximation errors that manifest rare extreme events and we propagate their effects through iterations. We establish probabilistic asymptotic and non-asymptotic convergence bounds as functions of the range (upper/lower bounds) and variance of approximation errors. We use the derived bound to assess AxPGD in a sparse model predictive control of a spacecraft system and compare its accuracy with previously derived bounds.
Cite
@article{arxiv.2306.16964,
title = {Improved Convergence Bounds For Operator Splitting Algorithms With Rare Extreme Errors},
author = {Anis Hamadouche and Andrew M. Wallace and Joao F. C. Mota},
journal= {arXiv preprint arXiv:2306.16964},
year = {2023}
}