TY - JOUR

T1 - Method of alternating projections for the general absolute value equation

AU - Alcantara, Jan Harold

AU - Chen, Jein Shan

AU - Tam, Matthew K.

N1 - Funding Information:
J. H. Alcantara and J.-S. Chen’s research is supported by Ministry of Science and Technology, Taiwan. M. K. Tam is supported in part by DE200100063 from the Australian Research Council. This work was conducted while J. H. Alcantara was a postdoctoral fellow at National Taiwan Normal University. The authors would like to thank the anonymous referee for the valuable feedback and comments.
Funding Information:
J. H. Alcantara and J.-S. Chen’s research is supported by Ministry of Science and Technology, Taiwan. M. K. Tam is supported in part by DE200100063 from the Australian Research Council. This work was conducted while J. H. Alcantara was a postdoctoral fellow at National Taiwan Normal University. The authors would like to thank the anonymous referee for the valuable feedback and comments.
Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

PY - 2023/2

Y1 - 2023/2

N2 - A novel approach for solving the general absolute value equation Ax+ B| x| = c where A,B∈IRm×n and c∈IRm 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.

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

KW - Absolute value equation

KW - alternating projections

KW - fixed point sets

UR - http://www.scopus.com/inward/record.url?scp=85145400889&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85145400889&partnerID=8YFLogxK

U2 - 10.1007/s11784-022-01026-8

DO - 10.1007/s11784-022-01026-8

M3 - Article

AN - SCOPUS:85145400889

SN - 1661-7738

VL - 25

JO - Journal of Fixed Point Theory and Applications

JF - Journal of Fixed Point Theory and Applications

IS - 1

M1 - 39

ER -