Decentralized Multi-Agent Optimization Based on a Penalty Method

We propose a decentralized penalty method for general convex constrained multi-agent optimization problems. Each auxiliary penalized problem is solved approximately with a special parallel descent splitting method. The method can be implemented in a computational network where each agent sends information only to the nearest neighbours. Convergence of the method is established under rather weak assumptions. We also describe a specialization of the proposed approach to the feasibility problem.