The Error and Perturbation Bounds of the General Absolute Value Equations

Cui-Xia Li () and Shi-Liang Wu ()
Additional contact information
Cui-Xia Li: Yunnan Normal University
Shi-Liang Wu: Yunnan Normal University

Journal of Optimization Theory and Applications, 2025, vol. 205, issue 3, No 12, 21 pages

Abstract: Abstract To our knowledge, the error and perturbation bounds of the general absolute value equations (AVE) are not discussed. In order to fill in this study gap, in this paper, by introducing a class of absolute value functions, we study the error and perturbation bounds of these two AVEs: $$Ax-B|x|=b$$ A x - B | x | = b and $$Ax-|Bx|=b$$ A x - | B x | = b . Some useful error bounds and perturbation bounds of the above two AVEs are provided. Without limiting the matrix type, some computable estimates for the relevant upper bounds are given. By applying the absolute value equations, a new approach for some existing perturbation bounds of the linear complementarity problem (LCP) in (SIAM J. Optim., 18 (2007) 1250-1265) is provided. Some numerical examples for the AVEs from the LCP are given to show the feasibility of the perturbation bounds.

Keywords: Absolute value equations; The error bound; The perturbation bound; Linear complementarity problem; 65G50; 90C33 (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10957-025-02669-6 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:205:y:2025:i:3:d:10.1007_s10957-025-02669-6

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-025-02669-6

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().