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Absolute value equations

Authors
Journal
Linear Algebra and its Applications
0024-3795
Publisher
Elsevier
Publication Date
Volume
419
Identifiers
DOI: 10.1016/j.laa.2006.05.004
Keywords
  • Absolute Value Equations
  • Linear Complementarity Problems
Disciplines
  • Mathematics

Abstract

Abstract We investigate existence and nonexistence of solutions for NP-hard equations involving absolute values of variables: Ax − ∣ x∣ = b, where A is an arbitrary n × n real matrix. By utilizing an equivalence relation to the linear complementarity problem (LCP) we give existence results for this class of absolute value equations (AVEs) as well as a method of solution for special cases. We also give nonexistence results for our AVE using theorems of the alternative and other arguments.

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