We investigate a nonconvex, nonsmooth optimization approach based on DC (Difference of Convex functions) programming and DCA (DC Algorithm) for the so-called DC fitting problem, which aims to fit a given set of data points by a DC function. The problem is tackled as minimizing the squared Euclidean norm fitting error. It is formulated as a DC program for which a standard DCA scheme is developed. Furthermore, a modified DCA scheme with successive DC decomposition is proposed. These standard/modified versions of DCA are applied for solving the continuous piecewise-linear fitting problem. Numerical experiments on many synthetic and real datasets with small-to-large sizes show the efficiency of our DCA-based approach in comparison with the existing approaches for constructing continuous piecewise-linear models.

我们研究一种基于DC（凸函数的差异）编程和DCA（DC算法）的非凸，非平滑优化方法，用于所谓的DC拟合问题，该问题旨在通过DC函数拟合给定的数据点集。解决该问题的方法是最小化平方的欧几里得范数拟合误差。它被制定为DC程序，并为此开发了标准的DCA方案。此外，提出了一种具有连续DC分解的改进DCA方案。这些标准/修改版的DCA用于解决连续分段线性拟合问题。在许多从小到大的合成和真实数据集上的数值实验表明，与现有的构建连续分段线性模型的方法相比，基于DCA的方法的效率更高。