Distributed Optimization of Quadratic Costs with a Group-Sparsity Regularization Via PDMM

Structural sparsity is useful for variable and node selection in distributed networks. In this paper, we propose a distributed algorithm to solve the problem of a quadratic cost function with mixed $\ell_{1,2}$ -norm regularization to promote the group-sparsity of the solution. By introducing virtual pair nodes to each actual node and by decomposing the cost function to each nodes, we obtain a distributed optimization problem on an extended graph model, which is further solved via the PDMM algorithm. Numerical simulation results illustrate the accurate convergence of the proposed algorithm to the centralized solution.