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 - 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

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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 -