Circumcentering the Douglas–Rachford method
Circumcentering the Douglas–Rachford method
复制标题
圆心道格拉斯-拉赫福德方法
DOI：
10.1007/s11075-017-0399-5
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发表时间：
2017
影响因子：
2.1
通讯作者：
L. Santos
中科院分区：
文献类型：
--
作者：
R. Behling;Yunier Bello Cruz;L. Santos
我们介绍和研究了一种对Douglas-Rachford方法的几何修正，称为环绕中心-Douglas-Rachford方法。这种方法通过取反射步骤的平分线的交点来迭代求解某些类别的可行性问题。对两个仿射空间的最佳逼近问题进行了收敛分析，理论和数值结果均优于原Douglas-Rachford方法。在适当的条件下，证明了圆心-道格拉斯-拉克福德方法的线性收敛速度至少是仿射子空间之间的Friedrichs角的余弦，这是已知的道格拉斯-拉克福德方法的最快收敛速度。我们还初步讨论了圆心-道格拉斯-拉赫福德方法在多集情形和具有非仿射凸集的例子中的应用。
We introduce and study a geometric modification of the Douglas–Rachford method called the Circumcentered–Douglas–Rachford method. This method iterates by taking the intersection of bisectors of reflection steps for solving certain classes of feasibility problems. The convergence analysis is established for best approximation problems involving two (affine) subspaces and both our theoretical and numerical results compare favorably to the original Douglas–Rachford method. Under suitable conditions, it is shown that the linear rate of convergence of the Circumcentered–Douglas–Rachford method is at least the cosine of the Friedrichs angle between the (affine) subspaces, which is known to be the sharp rate for the Douglas–Rachford method. We also present a preliminary discussion on the Circumcentered–Douglas–Rachford method applied to the many set case and to examples featuring non-affine convex sets.
影响因子：
5.4
作者：
Hesse, Robert;Luke, D. Russell;Neumann, Patrick
通讯作者：
Neumann, Patrick