论文标题
具有能量和动量的梯度算法的动态行为
Dynamic behavior for a gradient algorithm with energy and momentum
论文作者
论文摘要
本文使用能量和动量研究了一种新型的梯度算法AGEM，以解决一般的非凸优化问题。研究了AGEM算法的解决方案性能，包括诸如统一界限和趋于临界点等方面。通过对高分辨率ODE系统的全面分析来研究动态行为。该ODE系统是非线性的，是通过遵守离散方案的限制来得出的，同时通过重新确定动量参数来保留动量效应。本文强调了ODE系统的全球体系良好，以及解决方案轨迹的时间呈现收敛性。此外，我们为遵守Polyak-lojasiewicz条件的目标函数建立了线性收敛速率。
This paper investigates a novel gradient algorithm, AGEM, using both energy and momentum, for addressing general non-convex optimization problems. The solution properties of the AGEM algorithm, including aspects such as uniformly boundedness and convergence to critical points, are examined. The dynamic behavior is studied through a comprehensive analysis of a high-resolution ODE system. This ODE system, being nonlinear, is derived by taking the limit of the discrete scheme while preserving the momentum effect through a rescaling of the momentum parameter. The paper emphasizes the global well-posedness of the ODE system and the time-asymptotic convergence of solution trajectories. Furthermore, we establish a linear convergence rate for objective functions that adhere to the Polyak-Łojasiewicz condition.
