An Optimal Algorithm for Strongly Convex Minimization under Affine Constraints

Adil Salim, Laurent Pierre Condat, Dmitry Kovalev, Peter Richtarik

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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.
Original languageEnglish (US)
Title of host publicationThe 25th International Conference on Artificial Intelligence and Statistics
PublisherarXiv
StatePublished - 2022

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