Method of alternating projections for the general absolute value equation

A novel approach for solving the general absolute value equation A x + B | x | = c where A , B ∈ I R m × n and c ∈ I R m is presented. We reformulate the equation as a nonconvex feasibility problem which we solve via the method of alternating projections (MAP). The fixed points set of the alternatin...

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Bibliographic Details
Published in:Journal of fixed point theory and applications Vol. 25; no. 1
Main Authors: Alcantara, Jan Harold, Chen, Jein-Shan, Tam, Matthew K.
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01.02.2023
Subjects:
Analysis
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
65K10
Absolute value equation
Primary 90-08
fixed point sets
alternating projections
ISSN:1661-7738, 1661-7746
Online Access:Get full text
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Summary:A novel approach for solving the general absolute value equation A x + B | x | = c where A , B ∈ I R m × n and c ∈ I R m is presented. We reformulate the equation as a nonconvex 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 local 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.
ISSN:1661-7738
1661-7746
DOI:10.1007/s11784-022-01026-8