Take $f=I_C$ and $h=I_D$. Their proximal maps are the <Euclidean projection onto a convex set>[projections] $P_C,P_D$, so
$$
w_{k+1}=w_k-P_Dw_k+P_C(2P_Dw_k-w_k).
$$
The Douglas--Rachford shadow sequence $P_Dw_k$ converges in finite dimensions to a point of $C\cap D$ when the intersection is nonempty.

Solution

Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 339 / 3 / c / i / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/iii/paper-339/3/c/i/solution