A New Distributed Constrained Multi-Agent Optimization Protocol with Convergence Proof via Exactness of Penalized Objective Function

This paper is concerned with distributed multiagent optimization with inequality and equality constraints based on exact penalty methods. In the literature of exact penalty methods, constrained optimization problem is solved through optimization of penalized objective function and, under mild assumptions, the set of the optimal solutions of the penalized objective function coincides with that of the original constrained optimization problem. Exploiting the exactness of the penalized objective function, this paper proposes a new distributed multi-agent optimization protocol which simplifies the update law of previous protocols based on exact penalty methods with equality constraints. Also more concrete proof of the convergence of the protocol is provided under the assumption of the exactness of the penalized objective function.