Accelerating continuous-time optimization with fixed-time time-varying second-order dynamics
Abstract
This paper proposes a new fixed-time second-order time-varying dynamics to accelerate continuous-time optimization. We derive a sufficient condition for the existence and uniqueness of solutions to a general ordinary differential equation (ODE) and present a rigorous proof establishing the well-posedness of our proposed algorithm, addressing a significant gap in the literature. We show that the time-varying coefficients in the proposed dynamics can be used to accelerate convergence speed to optimal solutions. The efficiency of the proposed method is demonstrated by numerical simulations on the ridge regression and training neural networks. © 2026 Journal of Nonlinear and Variational Analysis.
Fields of Study & Subjects
Extremum Seeking Control Systems
Advanced Control Systems Optimization
Advanced Optimization Algorithms Research
Publication details
- Journal / source
- Journal of Nonlinear and Variational Analysis
- Publisher
- Mathematical Research Press
- Volume
- 10
- Issue
- 3
- Publication date
- 28 March 2026
- Language
- EN