Presentation Information
[N-1-09]A Study on the Effect of Numerical Integration Accuracy
in the Discretization of the Dynamic Inertial Newton Method
◎Kurumi Inoue1, Ryo Yamatomi1, Hiroshi Ninomiya1 (1. shonan institute of technology)
Keywords:
Dynamical Inertial Newton Method,Optimization Algorithm,Heun Method
The Dynamical Inertial Newton (DIN) method is an optimization algorithm derived from a system of first-order ordinary differential equations and is typically discretized using the Forward Euler method. However, the first-order accuracy of the Forward Euler method may limit optimization performance due to discretization errors. In this study, we propose DIN Heun, which discretizes the DIN system using Heun’s method, a second-order numerical integration scheme. By utilizing the average of gradients at the current and predicted points, the proposed method achieves higher numerical integration accuracy.
To evaluate its effectiveness, numerical experiments were conducted on the two-dimensional Rosenbrock function. Experimental results showed that DIN Euler converged to an objective value of approximately 10⁻⁸, whereas DIN Heun reached approximately 10⁻¹², demonstrating improved optimization accuracy. These results suggest that enhancing numerical integration accuracy in the discretization of DIN can improve optimization performance.
To evaluate its effectiveness, numerical experiments were conducted on the two-dimensional Rosenbrock function. Experimental results showed that DIN Euler converged to an objective value of approximately 10⁻⁸, whereas DIN Heun reached approximately 10⁻¹², demonstrating improved optimization accuracy. These results suggest that enhancing numerical integration accuracy in the discretization of DIN can improve optimization performance.