A Primal Decomposition Approach to Globally Coupled Aggregative Optimization over Networks
Abstract
We consider a class of multiagent optimization problems, where each agent has a local objective function that depends on its own decision variables and the aggregate of others, and is willing to cooperate with other agents to minimize the sum of the local objectives. After associating each agent with an auxiliary variable and the related local estimates, we conduct primal decomposition to the globally coupled problem and reformulate it so that it can be solved distributedly. Based on the DouglasRachford method, an algorithm is proposed which ensures the exact convergence to a solution of the original problem. The proposed method enjoys desirable scalability by only requiring each agent to keep local estimates whose number grows linearly with the number of its neighbors. We illustrate our proposed algorithm by numerical simulations on a commodity distribution problem over a transport network.
 Publication:

arXiv eprints
 Pub Date:
 September 2021
 arXiv:
 arXiv:2109.12297
 Bibcode:
 2021arXiv210912297H
 Keywords:

 Electrical Engineering and Systems Science  Systems and Control;
 Mathematics  Optimization and Control