A Duality-Based Approach for Distributed Optimization with Coupling Constraints
For multi-agent systems needing to solve optimization problems with shared constraints, this provides a theoretically grounded distributed method.
This paper presents a distributed algorithm for convex optimization with coupling constraints, using duality theory to achieve a simple, intuitive update structure. Numerical results demonstrate its effectiveness.
In this paper we consider a distributed optimization scenario in which a set of agents has to solve a convex optimization problem with separable cost function, local constraint sets and a coupling inequality constraint. We propose a novel distributed algorithm based on a relaxation of the primal problem and an elegant exploration of duality theory. Despite its complex derivation based on several duality steps, the distributed algorithm has a very simple and intuitive structure. That is, each node solves a local version of the original problem relaxation, and updates suitable dual variables. We prove the algorithm correctness and show its effectiveness via numerical computations.