Proximal minimization based distributed convex optimization

We provide a novel iterative algorithm for distributed convex optimization over time-varying multi-agent networks, in the presence of heterogeneous agent constraints. We adopt a proximal minimization perspective and show that this set-up allows us to bypass the difficulties of existing algorithms while simplifying the underlying mathematical analysis. At every iteration each agent makes a tentative decision by solving a local optimization program, and then communicates this decision with neighboring agents. We show that following this scheme agents reach consensus on a common decision vector, and in particular that this vector is an optimizer of the centralized problem.