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

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,...

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Bibliographic Details
Published inJournal 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
LanguageEnglish
Published New York Springer US 09.09.2024
Springer Nature B.V
Subjects
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Dynamical systems
Engineering
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
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Summary: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.
ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-024-02525-z