Second-order Dynamical Systems with Fixed-time Convergence for Fixed Points of Lipschitz Operators
Year: 2026
Type: article
Abstract: This paper is devoted to developing novel second-order time-varying dynamical systems with fixed-time convergence for nonsmooth optimization problems. We first propose a second-order dynamical system to locate a fixed point of Lipschitz continuous operators within a fixed time. The existence and uniqueness of solutions for this dynamical system are established, followed by a convergence analysis through the construction of a Lyapunov function. We then present an alternative second-order fixed-time convergent dynamical system for finding the fixed point of contraction operators, which not only features a simpler structure but also offers more flexible parameters. Finally, we employ the proposed dynamical systems to solve both generalized monotone inclusion problems and nonsmooth additive composite optimization problems.
Source: Journal of Scientific Computing
Authors: Lien T. Nguyen, Andrew Eberhard, Xinghuo Yu, Chaojie Li
Institutions: RMIT University, UNSW Sydney
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,290
Funder: Australian Research Council
OpenAlex ID: W7156032124