The Douglas--Rachford Algorithm for Two (Not Necessarily Intersecting) Affine Subspaces
研究了当两个集合为不一定相交的仿射子空间时，Douglas-Rachford算法的迭代行为，证明了影子序列强收敛到最近的广义解，将已有结果从一致情形推广到非一致情形。
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.