Optimal Subgradient Methods for Lipschitz Convex Optimization with Error Bounds

Fuente: arXiv
Saved in:
Bibliographic Details
Main Author: Wang, Alex L.
Format: Preprint
Published: 2025
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866911321956548608
author Wang, Alex L.
author_facet Wang, Alex L.
contents We study the iteration complexity of Lipschitz convex optimization problems satisfying a general error bound. We show that for this class of problems, subgradient descent with either Polyak stepsizes or decaying stepsizes achieves minimax optimal convergence guarantees for decreasing distance-to-optimality. The main contribution is a novel lower-bounding argument that produces hard functions simultaneously satisfying zero-chain conditions and global error bounds.
format Preprint
id arxiv_https___arxiv_org_abs_2512_13863
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Optimal Subgradient Methods for Lipschitz Convex Optimization with Error Bounds
Wang, Alex L.
Optimization and Control
90C60, 90C25, 90C30
We study the iteration complexity of Lipschitz convex optimization problems satisfying a general error bound. We show that for this class of problems, subgradient descent with either Polyak stepsizes or decaying stepsizes achieves minimax optimal convergence guarantees for decreasing distance-to-optimality. The main contribution is a novel lower-bounding argument that produces hard functions simultaneously satisfying zero-chain conditions and global error bounds.
title Optimal Subgradient Methods for Lipschitz Convex Optimization with Error Bounds
topic Optimization and Control
90C60, 90C25, 90C30
url https://arxiv.org/abs/2512.13863