Protocol for Constrained Multi-Agent Optimization with Arbitrary Local Solvers

In constrained multi-agent optimization over a peer-to-peer digraph, each agent has his own decision variables that should be set as to cooperatively minimize the sum of local objective functions and subject to local constraint sets as well as globally coupling constraints. In this paper, we propose a general distributed cutting-plane consensus (DCPC) solution protocol that admits heterogeneous local solvers based on dual decomposition, whereby: i) individual agents can perform their optimization locally through their own local solvers which are not required to be ideal or identical; ii) agents can implement computation and communication at their own paces, using the messages of neighbors which are possibly out-dated; and iii) termination of the local computation is triggered by a collection of local stopping criterion for individual processors. We prove that the solution protocol achieves consensus on the optimal solution to the constrained multi-agent optimization under minimal inter-processor synchronization requirement. An application example of coordinated charging of plug-in electric vehicles is provided. Numerical results demonstrate the effectiveness of the proposed protocol and validate our theoretical findings.