Method of Alternating Projection for the Absolute Value Equation

Abstract

A novel approach for solving the general absolute value equation Ax + B|x| = c where A, B ∈ IR m×n and c ∈ IR 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.