一类由拟非扩张算子控制的非自治发展方程的渐近性
Asymptotic behavior of a nonautonomous evolution equation governed by a quasi-nonexpansive operator
摘要：
研究了希尔伯特空间中由拟非扩张算子控制的非自治发展方程的轨线的渐近性态。利用李雅普诺夫分析证明了该轨道弱收敛于算子的一个不动点。在度量次正则性条件下，我们进一步推导出了轨迹到不动点集的距离的灵活的全局指数型速率。所得到的结果被应用于分析自适应Douglas-Rachford动力系统的轨迹的渐近行为，该系统被应用于寻找两个算子之和的零点，其中一个是强单调的，而另一个是弱单调的。
英文摘要：
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.
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