# An Improved Boosted DC Algorithm for Nonsmooth Functions with Applications in Image Recovery

arXiv: https://arxiv.org/abs/2602.04237 · HTML: https://mlsanity.com/paper/2602.04237/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 55 references that are in the map.
- First posted on arXiv 4 Feb 2026.

## Builds on (most cited first, 9 of 9)

- [Accelerating the DC algorithm for smooth functions](https://mlsanity.com/paper/1507.07375/) (2015)
- [CDiNN -Convex Difference Neural Networks](https://mlsanity.com/paper/2103.17231/) (2021)
- [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)
- [A Boosted-DCA with Power-Sum-DC Decomposition for Linearly Constrained Polynomial Programs](https://mlsanity.com/paper/2205.02571/) (2022)
- [On Quadratic Convergence of DC Proximal Newton Algorithm for Nonconvex Sparse Learning in High Dimensions](https://mlsanity.com/paper/1706.06066/) (2017)
- [A DC Programming Approach for Solving Multicast Network Design Problems via the Nesterov Smoothing Technique](https://mlsanity.com/paper/1709.03062/) (2017)
- [High-order Moment Portfolio Optimization via An Accelerated Difference-of-Convex Programming Approach and Sums-of-Squares](https://mlsanity.com/paper/1906.01509/) (2019)
- [Boosted scaled subgradient method for DC programming](https://mlsanity.com/paper/2103.10757/) (2021)

## Abstract (arXiv)

We propose a new approach to perform the boosted difference of convex functions algorithm (BDCA) on non-smooth and non-convex problems involving the difference of convex (DC) functions. The recently proposed BDCA uses an extrapolation step from the point computed by the classical DC algorithm (DCA) via a line search procedure in a descent direction to get an additional decrease of the objective function and accelerate the convergence of DCA. However, when the first function in DC decomposition is non-smooth, the direction computed by BDCA can be ascent and a monotone line search cannot be performed. In this work, we proposed a monotone improved boosted difference of convex functions algorithm (IBDCA) for certain types of non-smooth DC programs, namely those that can be formulated as the difference of a possibly non-smooth function and a smooth one. We show that any cluster point of the sequence generated by IBDCA is a critical point of the problem under consideration and that the corresponding objective value is monotonically decreasing and convergent. We also present the global convergence and the convergent rate under the Kurdyka-Lojasiewicz property. The applications of IBDCA in image recovery show the effectiveness of our proposed method. The corresponding numerical experiments demonstrate that our IBDCA outperforms DCA and other state-of-the-art DC methods in both computational time and number of iterations.