Perturbed Fenchel Duality and Primal-Dual Convergence of First-Order Methods
Optimization and Control
2024-12-04 v2
Abstract
It has been shown that many first-order methods satisfy the perturbed Fenchel duality inequality, which yields a unified derivation of convergence. More first-order methods are discussed in this paper, e.g., dual averaging and bundle method. We show primal-dual convergence of them on convex optimization by proving the perturbed Fenchel duality property. We also propose a single-cut bundle method for saddle problem, and prove its convergence in a similar manner.
Keywords
Cite
@article{arxiv.2411.09503,
title = {Perturbed Fenchel Duality and Primal-Dual Convergence of First-Order Methods},
author = {Tiantian Zhao},
journal= {arXiv preprint arXiv:2411.09503},
year = {2024}
}
Comments
There was an error in the proof of convergence rate for subgradient method in Appendix B and C, and the perturbed Fenchel duality property was not used