An approximate dual subgradient algorithm for multi-agent non-convex optimization

TL;DR

This paper introduces a distributed approximate dual subgradient algorithm for multi-agent non-convex optimization problems with global constraints, allowing agents to converge to primal-dual solutions despite non-convexity and intermittent communication.

Contribution

It presents a novel distributed algorithm that handles non-convex objectives and constraints, relaxing consensus requirements and ensuring convergence under specific conditions.

Findings

Algorithm successfully converges to primal-dual solutions in non-convex settings.

Performance comparison shows advantages over existing algorithms.

Applicable to source localization problems with promising results.

Abstract

We consider a multi-agent optimization problem where agents subject to local, intermittent interactions aim to minimize a sum of local objective functions subject to a global inequality constraint and a global state constraint set. In contrast to previous work, we do not require that the objective, constraint functions, and state constraint sets to be convex. In order to deal with time-varying network topologies satisfying a standard connectivity assumption, we resort to consensus algorithm techniques and the Lagrangian duality method. We slightly relax the requirement of exact consensus, and propose a distributed approximate dual subgradient algorithm to enable agents to asymptotically converge to a pair of primal-dual solutions to an approximate problem. To guarantee convergence, we assume that the Slater's condition is satisfied and the optimal solution set of the dual limit is singleton. We implement our algorithm over a source localization problem and compare the performance with existing algorithms.