I'm trying to self-study the ADMM algorithm and came across this problem. The problem states:
"Consider finding a point of intersection of 2 convex sets $C,D\subseteq \mathbb{R} ^{n}$ via solving:
$\min _{x} \delta _{C}\left( x\right)+\delta _{D}\left( x\right)$, where $\delta _{C}$ and $\delta _{D}$ is the indicator function for the set C and D respectively.
Transform the above problem into the 2-block separable structure that ADMM can handle."
Before I transform the problem into the ADMM structure, how does minimising the indicator function allow me to find the point of intersection of the 2 sets? Is there an intuitive explanation for this formula?