# A Refined Inertial DC Algorithm for DC Programming

arXiv: https://arxiv.org/abs/2104.14750 · HTML: https://mlsanity.com/paper/2104.14750/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 45 references that are in the map.
- First posted on arXiv 30 Apr 2021.

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

- [Inertial Proximal Alternating Linearized Minimization (iPALM) for Nonconvex and Nonsmooth Problems](https://mlsanity.com/paper/1702.02505/) (2017)
- [iPiano: Inertial Proximal Algorithm for Non-Convex Optimization](https://mlsanity.com/paper/1404.4805/) (2014)
- [Computing B-Stationary Points of Nonsmooth DC Programs](https://mlsanity.com/paper/1511.01796/) (2015)
- [A proximal difference-of-convex algorithm with extrapolation](https://mlsanity.com/paper/1612.06265/) (2016)
- [Convex-Concave Backtracking for Inertial Bregman Proximal Gradient Algorithms in Non-Convex Optimization](https://mlsanity.com/paper/1904.03537/) (2019)
- [Accelerating the DC algorithm for smooth functions](https://mlsanity.com/paper/1507.07375/) (2015)
- [The Boosted DC Algorithm for linearly constrained DC programming](https://mlsanity.com/paper/1908.01138/) (2019)
- [A refined convergence analysis of pDCAe with applications to simultaneous sparse recovery and outlier detection](https://mlsanity.com/paper/1804.07213/) (2018)
- [The Boosted DC Algorithm for nonsmooth functions](https://mlsanity.com/paper/1812.06070/) (2018)

## Abstract (arXiv)

In this paper we consider the difference-of-convex (DC) programming problems, whose objective function is the difference of two convex functions. The classical DC Algorithm (DCA) is well-known for solving this kind of problems, which generally returns a critical point. Recently, an inertial DC algorithm (InDCA) equipped with heavy-ball inertial-force procedure was proposed in de Oliveira et al. (Set-Valued and Variational Analysis 27(4):895--919, 2019), which potentially helps to improve both the convergence speed and the solution quality. Based on InDCA, we propose a refined inertial DC algorithm (RInDCA) equipped with enlarged inertial step-size compared with InDCA. Empirically, larger step-size accelerates the convergence. We demonstrate the subsequential convergence of our refined version to a critical point. In addition, by assuming the Kurdyka-Lojasiewicz (KL) property of the objective function, we establish the sequential convergence of RInDCA. Numerical simulations on checking copositivity of matrices and image denoising problem show the benefit of larger step-size.