# A Nonmonotone Descent Method for Optimization Problems Defined by Upper-C2  Functions over Submanifolds

arXiv: https://arxiv.org/abs/2605.26909 · HTML: https://mlsanity.com/paper/2605.26909/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 May 2026.

## 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)

We consider the optimization problem of minimizing a nonsmooth function characterized by a nonsmooth formulation of the descent lemma over a manifold. In the unconstrained case over a Euclidean space, this class of functions is called upper-C2. Using the recent notion of projectional subdifferentials, we show that their descent property carries over to submanifolds. We propose a nonmonotone subgradient method to solve these problems and prove stationarity of accumulation points of the generated sequence as well as convergence and rate-of-convergence results under the Kurdyka-Lojasiewicz property. We also perform numerical experiments and show how our approach can be applied to a certain type of difference of convex functions as well as clustering problems on manifolds.