THE DOUGLAS-RACHFORD ALGORITHM FOR TWO (NOT NECESSARILY INTERSECTING) AFFINE SUBSPACES
THE DOUGLAS-RACHFORD ALGORITHM FOR TWO (NOT NECESSARILY INTERSECTING) AFFINE SUBSPACES
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DOI：
10.1137/15m1016989
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发表时间：
2016-01-01
影响因子：
3.1
通讯作者：
Moursi, Walaa M.
中科院分区：
文献类型：
--
作者：
Bauschke, Heinz H.;Moursi, Walaa M.
Douglas-Rachford算法是求解单调算子和的零点的一种经典的非常成功的分裂方法。当底层算子是正规锥算子时，该算法解决了一个凸可行性问题。在本文中，我们提供了一个详细的研究道格拉斯-Rachford迭代和相应的影子序列时，集是仿射子空间，不一定相交。我们证明了强收敛的阴影到最近的广义解。我们的结果扩展了最近的工作，从一致的情况下，不一致的情况下。提供了各种示例来说明结果。
The Douglas-Rachford algorithm is a classical and very successful splitting method for finding the zeros of the sums of monotone operators. When the underlying operators are normal cone operators, the algorithm solves a convex feasibility problem. In this paper, we provide a detailed study of the Douglas-Rachford iterates and the corresponding shadow sequence when the sets are affine subspaces that do not necessarily intersect. We prove strong convergence of the shadows to the nearest generalized solution. Our results extend recent work from the consistent case to the inconsistent case. Various examples are provided to illustrates the results.