Distributed Computation for Sparse Optimization with Linear Equality Constraints

In this paper, we propose two distributed algorithms for sparse optimization problems with linear equality constraints of the vector case and the matrix case. In the l
₁
-norm minimization with the linear algebraic equation constraint, we take the general block partition for the information matrix. In the l
_2,1
-norm minimization with the linear operator constraint, we mainly focus on the case that every node holds the local linear constraint, while the case that all nodes have a coupling constraint can be easily obtained in a similar way. The two algorithms are both based on the primal-dual subgradient method and derivative feedback techniques. Finally, we investigate the convergence properties for the proposed algorithms, and then numerical examples are given to verify the algorithms.