DCA with Successive DC Decomposition for Convex Piecewise-Linear Fitting

Abstract

We study an approach based on DC (Difference of Convex functions) programming and DCA (DC Algorithm) for the convex piecewise-linear fitting problem. The objective is to fit a given set of data points by a convex piecewise-linear function. The problem is formulated as minimizing the squared \(\ell _2\)-norm fitting error, and then reformulated as a DC program for which a standard DCA scheme is applied. Furthermore, a modified DCA scheme with successive DC decomposition is proposed with the aim to improve DCA by updating the convex approximation of the fitting error function during DCA iterations. These DCAs consist in solving a sequence of convex quadratic programs. Moreover, the modified DCA still has the same convergence properties as the standard DCA. Numerical results on synthetic/real datasets show the efficiency of our methods when comparing with the existing approaches.