An Optimal Algorithm for Strongly Convex Minimization under Affine Constraints
Optimization and Control
2022-04-12 v3
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
@article{arxiv.2102.11079,
title = {An Optimal Algorithm for Strongly Convex Minimization under Affine Constraints},
author = {Adil Salim and Laurent Condat and Dmitry Kovalev and Peter Richtárik},
journal= {arXiv preprint arXiv:2102.11079},
year = {2022}
}