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

• Published in: Journal of optimization theory and applications Vol. 203; no. 1; pp. 600 - 628
• Main Authors: Zhang, Xu, Li, Cailian, Zhang, Longcheng, Hu, Yaling, Peng, Zheng
• Format: Journal Article
• Language: English
• Published: New York Springer US 01-10-2024; Springer Nature B.V
• Subjects: Applications of Mathematics; Calculus of Variations and Optimal Control; Optimization; Convergence; Dynamical systems; Engineering; Equilibrium; Mathematics; Mathematics and Statistics; Operations Research/Decision Theory; Optimization; Theory of Computation; Global convergence; 65K05; Absolute value equations; 90C33; 65K10; Fixed-time stable; Global error bound; Dynamic method
• ISSN: 0022-3239; 1573-2878
• DOI: 10.1007/s10957-024-02525-z

Two new accelerated fixed-time stable dynamic systems are proposed for solving absolute value equations (AVEs):
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.