Convergence-Accelerated Fixed-Time Dynamical Methods for Absolute Value Equations

Xu Zhang, Cailian Li, Longcheng Zhang, Yaling Hu and Zheng Peng ()
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Xu Zhang: Xiangtan University
Cailian Li: Xiangtan University
Longcheng Zhang: Xiangtan University
Yaling Hu: Xiangtan University
Zheng Peng: Xiangtan University

Journal of Optimization Theory and Applications, 2024, vol. 203, issue 1, No 22, 600-628

Abstract: Abstract Two new accelerated fixed-time stable dynamic systems are proposed for solving absolute value equations (AVEs): $$Ax-|x|-b=0$$ A x - | x | - b = 0 . Under some mild conditions, the equilibrium point of the proposed dynamic systems is completely equivalent to the solution of the AVEs under consideration. Meanwhile, we have introduced a new relatively tighter global error bound for the AVEs. Leveraging this finding, we have separately established the globally fixed-time stability of the proposed methods, along with providing the conservative settling-time for each method. Compared with some existing state-of-the-art dynamical methods, preliminary numerical experiments show the effectiveness of our methods in solving the AVEs.

Keywords: Absolute value equations; Global error bound; Dynamic method; Fixed-time stable; Global convergence; 65K05; 65K10; 90C33 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10957-024-02525-z

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