Proximal bundle methods for hybrid weakly convex composite optimization problems
Optimization and Control
2026-05-19 v3
Abstract
This paper establishes the iteration-complexity of proximal bundle methods for solving hybrid (i.e., a blend of smooth and nonsmooth) weakly convex composite optimization (HWC-CO) problems. This is done in a unified manner by considering a proximal bundle framework (PBF), which includes various well-known bundle update schemes. In contrast to hard-to-check stationary conditions (e.g., the Moreau stationarity) used by other methods for solving HWC-CO, PBF uses a stationarity measure that is easily verifiable.
Cite
@article{arxiv.2303.14896,
title = {Proximal bundle methods for hybrid weakly convex composite optimization problems},
author = {Jiaming Liang and Renato D. C. Monteiro and Honghao Zhang},
journal= {arXiv preprint arXiv:2303.14896},
year = {2026}
}
Comments
28 pages, first revision: December 26, 2024, second revision: May 16, 2026