A Cutting Plane-Based Distributed Algorithm for Non-Smooth Optimisation With Coupling Constraints

In this letter, we study a general setup for constrained convex optimisation over time-varying networks. We propose a distributed algorithm, based on the cutting plane method, to address non-smooth optimisation challenges. Cutting plane-based approaches require constraint consensus which is structurally different from established consensus schemes. We bridge this gap by linking the cutting plane-based algorithm with a dynamic average tracking scheme. The distributed cutting plane algorithm is presented and its convergence is analysed. Its performance is investigated through a numerical example.