Operations Research Seminar: Kostas Margellos

Proximal algorithms for distributed optimisation over uncertain networks

Kostas MARGELLOS, University of Oxford

In this talk we provide a proximal minimization based algorithm for distributed convex optimization over time- varying multi-agent networks, in the presence of constraints and uncertainty. We first focus on the deterministic case, develop an iterative algorithm and show that agents reach consensus, and in particular, that they convergence to some optimizer of the centralized problem. Our approach is then extended to the case where the agents’ constraint sets are affected by a possibly common uncertainty vector. To tackle this problem we follow a scenario-based methodology and offer probabilistic guarantees regarding the feasibility properties of the resulting solution. We illustrate how this distributed methodology can be applied to the problem of energy management in building networks affected by stochastic uncertainty.