THIS PAPER IS ELIGIBLE FOR THE STUDENT PAPER AWARD. Clustered cell-free networking emerges as a promising paradigm for future communication systems. We utilize the sum ergodic capacity for the optimization problem, which stands as an appropriate performance metric for such systems. However, the networking aspect leads to a difficult combinatorial problem. Moreover, the implicitness of ergodic capacity results in obstacles to evaluation and optimization. Existing works often rely on inaccurate approximations of ergodic capacity and/or high-cost integer programming~(IP) algorithms, rendering them impractical for real-world deployment. In this paper, we formulate the problem as an IP problem and relax it into a continuous one with the ergodic capacity approximated by deterministic equivalents. Importantly, we establish the tightness of the relaxation without sacrificing the optimality of the solution. We then employ Bregman proximal gradient (BPG) nested with Dykstra’ s algorithm to solve the relaxed problem and show the convergence for both BPG and its subproblems. Simulation results verify the effectiveness and efficiency of our approach.