论文标题
在道格拉斯 - 拉赫福德操作员的最低位移矢量
On the Minimal Displacement Vector of the Douglas-Rachford Operator
论文作者
论文摘要
道格拉斯 - 拉赫福德算法可以表示为坚定的非专业操作员的固定点迭代。当操作员没有固定点时，算法的迭代差异，但是连续迭代之间的差异会收敛到所谓的最小位移矢量，该矢量可用于证明优化问题的不可行性。在本文中，我们建立了最小位移向量的新属性，这使我们能够概括一些现有结果。
The Douglas-Rachford algorithm can be represented as the fixed point iteration of a firmly nonexpansive operator. When the operator has no fixed points, the algorithm's iterates diverge, but the difference between consecutive iterates converges to the so-called minimal displacement vector, which can be used to certify infeasibility of an optimization problem. In this paper, we establish new properties of the minimal displacement vector, which allow us to generalize some existing results.
