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Lien T. Nguyen, Andrew Eberhard, Xinghuo Yu, Chaojie Li, Accelerating continuous-time optimization with fixed-time time-varying second-order dynamics

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DOI: 10.23952/jnva.10.2026.3.02

Volume 10, Issue 3, 1 June 2026, Pages 507-521

 

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.

 

How to Cite this Article:
L. T. Nguyen, A. Eberhard, X. Yu, C. Li, Accelerating continuous-time optimization with fixed-time time-varying second-order dynamics, J. Nonlinear Var. Anal. 10 (2026), 507-521.