The proximal methods for solving absolute value equation

Abstract

In this paper, by considering that the objective function of the least squares NP-hard absolute value equations (AVE) \begin{document}$ Ax-\vert x\vert = b $\end{document} , is non-convex and non-smooth, two types of proximal algorithms are proposed to solve it. One of them is the proximal difference-of-convex algorithm with extrapolation and another is the proximal subgradient method. The convergence results of the proposed methods are proved under certain assumptions. Moreover, a numerical comparison is presented to demonstrate the effectiveness of the suggested methods.