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arXiv · 2106.03268

Method of Alternating Projection for the Absolute Value Equation

Jan Harold Alcantara·Jein-Shan Chen·Matthew K. Tam
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Abstract

A novel approach for solving the general absolute value equation $Ax+B|x| = c$ where $A,B\in \mathbb{R}^{m\times n}$ and $c\in \mathbb{R}^m$ is presented. We reformulate the equation as a feasibility problem which we solve via the method of alternating projections (MAP). The fixed points set of the alternating projections map is characterized under nondegeneracy conditions on $A$ and $B$. Furthermore, we prove linear convergence of the algorithm. Unlike most of the existing approaches in the literature, the algorithm presented here is capable of handling problems with $m\neq n$, both theoretically and numerically.

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Jan Harold Alcantara, Jein-Shan Chen, Matthew K. Tam. 2021-06-06. Method of Alternating Projection for the Absolute Value Equation. https://arxiv.org/abs/2106.03268

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