论文标题
非自主进化方程的渐近行为，由准北方运算符支配
Asymptotic behavior of a nonautonomous evolution equation governed by a quasi-nonexpansive operator
论文作者
论文摘要
我们研究了由希尔伯特空间中的准北方运营商控制的非自主进化方程轨迹的渐近行为。我们通过依赖Lyapunov分析来证明轨迹轨迹较弱的趋势。在度量次级条件下，我们进一步得出了轨迹与固定点集的距离的柔性全局指数型速率。获得的结果用于分析自适应Douglas-Rachford动力系统的轨迹的渐近行为，该系统用于查找两个操作员的总和的零，其中一个是强烈单调的，而另一个是弱单调的。
We study the asymptotic behavior of the trajectory of a nonautonomous evolution equation governed by a quasi-nonexpansive operator in Hilbert spaces. We prove the weak convergence of the trajectory to a fixed point of the operator by relying on Lyapunov analysis. Under a metric subregularity condition, we further derive a flexible global exponential-type rate for the distance of the trajectory to the set of fixed points. The results obtained are applied to analyze the asymptotic behavior of the trajectory of an adaptive Douglas-Rachford dynamical system, which is applied for finding a zero of the sum of two operators, one of which is strongly monotone while the other one is weakly monotone.
