We introduce a novel adaptive damping technique for an inertial gradient system which finds application as a gradient descent algorithm for unconstrained optimisation. In an example using the non-convex Rosenbrock's function, we show an improvement on existing momentum-based gradient optimisation methods. Also using Lyapunov stability analysis, we demonstrate the performance of the continuous-time version of the algorithm. Using numerical simulations, we consider the performance of its discrete-time counterpart obtained by using the symplectic Euler method of discretisation.
翻译:我们为惯性梯度系统引入了一种新的适应性障碍技术,该技术将应用作为不受限制的最佳化的梯度下限算法。在使用非曲线罗森布罗克功能的例子中,我们展示了现有动力梯度优化方法的改进。此外,我们使用Lyapunov稳定性分析,演示了该算法的连续时间版本的性能。我们使用数字模拟,考虑了通过使用静电电离析法获得的离散时间对应方的性能。