基于常微分方程的加速梯度算法

ccelerated gradient algorithm is an algorithm which has faster convergence rate than traditional gradient descent method on the premise of using only one step information in optimization problems. When the objective function is strongly convex, a new accelerating gradient algorithm is obtained by discretizing the high-resolution ordinary differential equations corresponding to Nesterov's accelerating gradient algorithm. After that, the new algorithm is compared with the symplectic accelerated gradient algorithm. The numerical result shows that the convergence rate of the new accelerated gradient algorithm is faster.