# Rate of Convergence of the Bundle Method

arXiv: https://arxiv.org/abs/1609.00842 · HTML: https://mlsanity.com/paper/1609.00842/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Sep 2016.

## Built on by (most cited first, 4 of 4)

- [Proximal Oracles for Optimization and Sampling](https://mlsanity.com/paper/2404.02239/) (2024)
- [Survey Descent: A Multipoint Generalization of Gradient Descent for Nonsmooth Optimization](https://mlsanity.com/paper/2111.15645/) (2021)
- [Gauges and Accelerated Optimization over Smooth and/or Strongly Convex Sets](https://mlsanity.com/paper/2303.05037/) (2023)
- [Linearly Convergent Algorithms for Nonsmooth Problems with Unknown Smooth Regions](https://mlsanity.com/paper/2507.19465/) (2025)

## Abstract (arXiv)

We prove that the bundle method for nonsmooth optimization achieves solution accuracy varepsilon in at most Obig(ln(1/varepsilon)/varepsilonbig) iterations, if the function is strongly convex. The result is true for the versions of the method with multiple cuts and with cut aggregation.