A Conservation Law Method in Optimization
This addresses optimization challenges in machine learning and scientific computing, though it appears incremental as it builds on existing physics-inspired methods.
The authors tackled nonconvex optimization by proposing algorithms that simulate Newton's Second Law without friction using a symplectic Euler scheme, achieving high-speed convergence as shown in experiments on various function types.
We propose some algorithms to find local minima in nonconvex optimization and to obtain global minima in some degree from the Newton Second Law without friction. With the key observation of the velocity observable and controllable in the motion, the algorithms simulate the Newton Second Law without friction based on symplectic Euler scheme. From the intuitive analysis of analytical solution, we give a theoretical analysis for the high-speed convergence in the algorithm proposed. Finally, we propose the experiments for strongly convex function, non-strongly convex function and nonconvex function in high-dimension.