An Optimal Algorithm for Strongly Convex Minimization Under Affine Constraints
Abstract
Optimization problems under affine constraints appear in various areas of machine learning. We consider the task of minimizing a smooth strongly convex function F(x) under the affine constraint Kx = b, with an oracle providing evaluations of the gradient of F and multiplications by K and its transpose. We provide lower bounds on the number of gradient computations and matrix multiplications to achieve a given accuracy. Then we propose an accelerated primal-dual algorithm achieving these lower bounds. Our algorithm is the first optimal algorithm for this class of problems.
Cite
Text
Salim et al. "An Optimal Algorithm for Strongly Convex Minimization Under Affine Constraints." Artificial Intelligence and Statistics, 2022.Markdown
[Salim et al. "An Optimal Algorithm for Strongly Convex Minimization Under Affine Constraints." Artificial Intelligence and Statistics, 2022.](https://mlanthology.org/aistats/2022/salim2022aistats-optimal/)BibTeX
@inproceedings{salim2022aistats-optimal,
title = {{An Optimal Algorithm for Strongly Convex Minimization Under Affine Constraints}},
author = {Salim, Adil and Condat, Laurent and Kovalev, Dmitry and Richtarik, Peter},
booktitle = {Artificial Intelligence and Statistics},
year = {2022},
pages = {4482-4498},
volume = {151},
url = {https://mlanthology.org/aistats/2022/salim2022aistats-optimal/}
}