DCA-based algorithms for DC fitting

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...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2021-06, Vol.389, p.113353, Article 113353
Main Authors: Ho, Vinh Thanh, Le Thi, Hoai An, Pham Dinh, Tao
Format: Article
Language:English
Subjects:
Computer Science
DC fitting
DC programming
DCA
DCA with successive DC decomposition
Piecewise-linear fitting
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Summary: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.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2020.113353