Distributed optimization for convex problem with coupling affine constraints.

Question

I have the following convex optimization problem $$ \begin{split} \min_{\tilde{q}}\; & ||\tilde{q} - r||_2^2\\ s.t. & A^T\tilde{q} \leq b \end{split} $$ where $\tilde{q} = [q_1;...;q_N]$ is vector that has subvectors $q_i$ inside. and I would like to solve in distributed way, or being more specific in parallel. I have the same number of computational nodes as a number of subvectors $q_i$ such that $q_i$ is computed at $i$th computational node. I have heard about consensus based optimization and it seems to fit my goal, but unfortunately, I cannot find material that can put problem above in distributed. In my mind I want to find an algorithm that is able to compute $q_1, q_2,...,q_N$ for different in parallel and then exchange some dual or auxiliary variables between nodes and recomputes variable again and so far and so on. Please, tell me algorithms with references that could be applicable here, including references to good papers or books. It would be amazing if somebody can even show me derivations to this problem. Thanks everyone for help!