A Lagrange Multiplier Method for Distributed Optimization Based on Multi-Agent Network With Private and Shared Information

In this paper, a Lagrange multiplier method is investigated for designing distributed optimization algorithm, which convergence is analyzed from the view of multi-agent networks with connected graphs. In the network, each agent is with both private and shared information. The shared information is shared with the agent’s neighbors via a network with a connected graph. Furthermore, a Lagrange-multiplier-based algorithm with parallel computing architecture is designed for distributed optimization. Under mild conditions, the convergence of the algorithm, corresponding to the consensus of the Lagrange multipliers, is presented and proved. The experiments with simulations are presented to illustrate the performance of the proposed method.