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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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
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Abstract	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.
AbstractList	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.
ArticleNumber	39
Author	Chen, Jein-Shan Alcantara, Jan Harold Tam, Matthew K.
Author_xml	– sequence: 1 givenname: Jan Harold surname: Alcantara fullname: Alcantara, Jan Harold organization: Institute of Statistical Sciences – sequence: 2 givenname: Jein-Shan orcidid: 0000-0002-4596-9419 surname: Chen fullname: Chen, Jein-Shan email: jschen@math.ntnu.edu.tw organization: Department of Mathematics, National Taiwan Normal University – sequence: 3 givenname: Matthew K. surname: Tam fullname: Tam, Matthew K. organization: School of Mathematics and Statistics, The University of Melbourne
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Snippet	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...
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SubjectTerms	Analysis Mathematical Methods in Physics Mathematics Mathematics and Statistics
Title	Method of alternating projections for the general absolute value equation
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