# Nonmonotone subgradient methods based on a local descent lemma

arXiv: https://arxiv.org/abs/2510.19341 · HTML: https://mlsanity.com/paper/2510.19341/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 50 references that are in the map.
- First posted on arXiv 22 Oct 2025.

## Builds on (most cited first, 10 of 10)

- [Accelerating the DC algorithm for smooth functions](https://mlsanity.com/paper/1507.07375/) (2015)
- [Forward-backward envelope for the sum of two nonconvex functions: Further properties and nonmonotone line-search algorithms](https://mlsanity.com/paper/1606.06256/) (2016)
- [The Boosted DC Algorithm for linearly constrained DC programming](https://mlsanity.com/paper/1908.01138/) (2019)
- [A boosted DC algorithm for non-differentiable DC components with non-monotone line search](https://mlsanity.com/paper/2111.01290/) (2021)
- [Qualitative Properties of the Minimum Sum-of-Squares Clustering Problem](https://mlsanity.com/paper/1810.02057/) (2018)
- [Using positive spanning sets to achieve d-stationarity with the Boosted DC Algorithm](https://mlsanity.com/paper/1907.11471/) (2019)
- [The Boosted Double-Proximal Subgradient Algorithm for Nonconvex Optimization](https://mlsanity.com/paper/2306.17144/) (2023)
- [Local Convergence Analysis of Augmented Lagrangian Methods for Piecewise Linear-Quadratic Composite Optimization Problems](https://mlsanity.com/paper/2010.11379/) (2020)
- [Coderivative-Based Semi-Newton Method in Nonsmooth Difference Programming](https://mlsanity.com/paper/2301.03491/) (2023)
- [Convergence of Augmented Lagrangian Methods for Composite Optimization Problems](https://mlsanity.com/paper/2307.15627/) (2023)

## Built on by (most cited first, 1 of 1)

- [A proximal subgradient method for nonconvex stochastic optimization under the Kurdyka-Lojasiewicz condition](https://mlsanity.com/paper/2608.05460/) (2026)

## Abstract (arXiv)

In this paper we present a nonmonotone line search subgradient algorithm tailored to upper-C2 functions. This is a family of nonsmooth and nonconvex functions that satisfies a nonsmooth and local version of the descent lemma, making them suitable for line searches. We prove subsequential convergence of the proposed algorithm to a stationary point of the optimization problem. Our approach allows us to cover the setting of various subgradient algorithms, including Newton and quasi-Newton methods. In addition, we propose a specification of the general scheme, named Self-adaptive Nonmonotone Subgradient Method (SNSM), which automatically updates the parameters of the line search. Particular attention is paid to the minimum sum-of-squares clustering problem, for which we provide a concrete implementation of SNSM. We conclude with some numerical experiments where we exhibit the advantages of SNSM in comparison with some known algorithms.