Preconditioned conjugate gradient methods for absolute value equations


  • Nassima Anane Universite Ferhat Abbas, Algeria
  • Mohamed Achache Universite Ferhat Abbas, Algeria



Absolute value equations, linear systems, unconstrained quadratic optimization, linear complementarity problems
Abstract views: 416


We investigate the NP-hard absolute value equations (AVE), \(Ax-B|x| =b\), where \(A,B\) are given symmetric matrices in \(\mathbb{R}^{n\times n}, \ b\in \mathbb{R}^{n}\).
By reformulating the AVE as an equivalent unconstrained convex quadratic optimization, we prove that the unique solution of the AVE is the unique minimum of the corresponding quadratic optimization. Then across the latter, we adopt the preconditioned conjugate gradient methods to determining an approximate solution of the AVE.
The computational results show the efficiency of these approaches in dealing with the AVE.


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How to Cite

Anane, N., & Achache, M. (2020). Preconditioned conjugate gradient methods for absolute value equations. J. Numer. Anal. Approx. Theory, 49(1), 3–14.