On distributed optimization under inequality constraints via Lagrangian primal-dual methods

We consider a multi-agent convex optimization problem where agents are to minimize a sum of local objective functions subject to a global inequality constraint and a global constraint set. To deal with this, we devise a distributed primal-dual subgradient algorithm which is based on the characterization of the primal-dual optimal solutions as the saddle points of the Lagrangian function. This algorithm allows the agents to exchange information over networks with time-varying topologies and asymptotically agree on a pair of primal-dual optimal solutions and the optimal value.