Projection-based Dynamics for Distributed Optimization Subject to General Constraints

This paper presents a continuous-time multi-agent system for distributed convex optimization problem subject to bound, equality, and inequality constraints. The individual dynamics of each agent is designed based on projection operator, subgradient operator, and consensus operator. All agents in the system communicate state information using a proportional-integral protocol. It is proved that all agents with any initial state can reach state consensus at an optimal solution to the given constrained optimization problem, provided that communication graph among agents is undirected and connected. Simulation results are presented to substantiate the theoretical results.