# A boosted DC algorithm for non-differentiable DC components with non-monotone line search

arXiv: https://arxiv.org/abs/2111.01290 · HTML: https://mlsanity.com/paper/2111.01290/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Nov 2021.

## Built on by (most cited first, 5 of 5)

- [Enforcing Fair Predicted Scores on Intervals of Percentiles by Difference-of-Convex Constraints](https://mlsanity.com/paper/2505.12530/) (2025)
- [Scalable DC Optimization via Adaptive Frank-Wolfe Algorithms](https://mlsanity.com/paper/2507.17545/) (2025)
- [Nonmonotone subgradient methods based on a local descent lemma](https://mlsanity.com/paper/2510.19341/) (2025)
- [An inexact LPA for DC composite optimization and application to matrix completions with outliers](https://mlsanity.com/paper/2303.16822/) (2023)
- [An Improved Boosted DC Algorithm for Nonsmooth Functions with Applications in Image Recovery](https://mlsanity.com/paper/2602.04237/) (2026)

## Abstract (arXiv)

We introduce a new approach to apply the boosted difference of convex functions algorithm (BDCA) for solving non-convex and non-differentiable problems involving difference of two convex functions (DC functions). Supposing the first DC component differentiable and the second one possibly non-differentiable, the main idea of BDCA is to use the point computed by the DC algorithm (DCA) to define a descent direction and perform a monotone line search to improve the decreasing the objetive function accelerating the convergence of the DCA. However, if the first DC component is non-differentiable, then the direction computed by BDCA can be an ascent direction and a monotone line search cannot be performed. Our approach uses a non-monotone line search in the BDCA (nmBDCA) to enable a possible growth in the objective function values controlled by a parameter. Under suitable assumptions, we show that any cluster point of the sequence generated by the nmBDCA is a critical point of the problem under consideration and provide some iteration-complexity bounds. Furthermore, if the first DC component is differentiable, we present different iteration-complexity bounds and prove the full convergence of the sequence under the Kurdyka-Lojasiewicz property of the objective function. Some numerical experiments show that the nmBDCA outperforms the DCA such as its monotone version.