In this note, we provide necessary and sufficient conditions that ensure the existence and uniqueness of solution of the general form of absolute value equations (AVEs), Ax−B|x|=b. The performed analysis is based on the equivalence between AVEs and horizontal linear complementarity problems (HLCPs). New sufficient conditions are proposed as well. We then compare the proposed conditions with recent results in the literature and we detail how efficient solution methods for HLCPs can be easily applied to the solution of general AVEs. Finally, we provide comments on the solvability of general AVEs under conditions larger than uniqueness of solution.
On the solution of general absolute value equations / Mezzadri, F.. - In: APPLIED MATHEMATICS LETTERS. - ISSN 0893-9659. - 107:(2020), pp. 1-7. [10.1016/j.aml.2020.106462]
On the solution of general absolute value equations
Mezzadri F.
2020
Abstract
In this note, we provide necessary and sufficient conditions that ensure the existence and uniqueness of solution of the general form of absolute value equations (AVEs), Ax−B|x|=b. The performed analysis is based on the equivalence between AVEs and horizontal linear complementarity problems (HLCPs). New sufficient conditions are proposed as well. We then compare the proposed conditions with recent results in the literature and we detail how efficient solution methods for HLCPs can be easily applied to the solution of general AVEs. Finally, we provide comments on the solvability of general AVEs under conditions larger than uniqueness of solution.
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