论文标题
部分可观测时空混沌系统的无模型预测
Second order splitting dynamics with vanishing damping for additively structured monotone inclusions
论文作者
论文摘要
在真正的希尔伯特空间的框架内，我们解决了找到最大单调操作员$ a $和cocoercive运算符$ b $的零的问题。我们研究了由二阶方程产生的轨迹的渐近行为，并消失了阻尼，附着在该问题上，并由时间依赖的前向式操作员支配。这是一个拆分系统，因为它仅需要$ b $的远期评估和$ a $的后退评估。对系统参数的正确调整可确保轨迹与$ a + b $的零集合的弱收敛，以及速度向零的快速收敛。我们系统的一种特殊情况允许在最小化适当，凸和较低的半连续功能的总和以及具有Lipschitz连续梯度的平滑凸功能的问题的问题中得出快速收敛速率。我们通过数值实验说明了理论结果。
In the framework of a real Hilbert space, we address the problem of finding the zeros of the sum of a maximally monotone operator $A$ and a cocoercive operator $B$. We study the asymptotic behaviour of the trajectories generated by a second order equation with vanishing damping, attached to this problem, and governed by a time-dependent forward-backward-type operator. This is a splitting system, as it only requires forward evaluations of $B$ and backward evaluations of $A$. A proper tuning of the system parameters ensures the weak convergence of the trajectories to the set of zeros of $A + B$, as well as fast convergence of the velocities towards zero. A particular case of our system allows to derive fast convergence rates for the problem of minimizing the sum of a proper, convex and lower semicontinuous function and a smooth and convex function with Lipschitz continuous gradient. We illustrate the theoretical outcomes by numerical experiments.
