Method of Alternating Projection for the Absolute Value Equation

2021/06/06 by Alcantara, Jan Harold, Chen, Jein-Shan, Tam, Matthew K.
#FOS: Mathematics #Numerical Analysis (math.NA) #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2106.03268

Abstract

A novel approach for solving the general absolute value equation Ax+B|x| = c where A,B∈ ℝ^{m× n} and c∈ 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≠ n, both theoretically and numerically.

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