English

Convergence rate analysis of the gradient descent-ascent method for convex-concave saddle-point problems

Optimization and Control 2022-09-19 v2

Abstract

In this paper, we study the gradient descent-ascent method for convex-concave saddle-point problems. We derive a new non-asymptotic global convergence rate in terms of distance to the solution set by using the semidefinite programming performance estimation method. The given convergence rate incorporates most parameters of the problem and it is exact for a large class of strongly convex-strongly concave saddle-point problems for one iteration. We also investigate the algorithm without strong convexity and we provide some necessary and sufficient conditions under which the gradient descent-ascent enjoys linear convergence.

Keywords

Cite

@article{arxiv.2209.01272,
  title  = {Convergence rate analysis of the gradient descent-ascent method for convex-concave saddle-point problems},
  author = {Moslem Zamani and Hadi Abbaszadehpeivasti and Etienne de Klerk},
  journal= {arXiv preprint arXiv:2209.01272},
  year   = {2022}
}
R2 v1 2026-06-28T00:39:36.172Z