Method of alternating projections for the general absolute value equation

Jan Harold Alcantara, Jein Shan Chen*, Matthew K. Tam

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


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.

Original languageEnglish
Article number39
JournalJournal of Fixed Point Theory and Applications
Issue number1
Publication statusPublished - 2023 Feb


  • Absolute value equation
  • alternating projections
  • fixed point sets

ASJC Scopus subject areas

  • Modelling and Simulation
  • Geometry and Topology
  • Applied Mathematics


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