I am struggling with the following alternating projection theorem tasks.
$ C_1$ , $C_2$ - closed convex subsets in $R^d$, their intersection is not empty.
$x_0 \in C$, and sequence of points $\{x_n\}$ is defined as $x_{n+1} = P_{C_1}P_{C_2}x_n$
Find $x^* \in R^d$ s.t: $||x^*|| \leq r, r>0$ and $Ax^* = y$,
where $A \in R^{k \times d}$, $k<d$, rank $A = k$
I need to write maths algorithm using the alternating projections theorem.
I have started by writing down a Lagrangian for the problem but got stuck at the formulation. Thanks in advance for some hints!