Distributed aggregative optimization with affine coupling constraints.

Abstract

This paper investigates a distributed aggregative optimization problem subject to coupling affine inequality constraints, in which local objective functions depend not only on their own decision variables but also on an aggregation of all the agents' variables. The formulated problem encompasses numerous practical applications, such as commodity distribution, electric vehicle charging, and energy consumption control in power grids. Hence, there is a compelling need to explore a new neurodynamic approach to address this. To this end, a novel distributed aggregative primal-dual algorithm is proposed based on the dual diffusion strategy and distributed tracking technique, which typically makes a slight yet important modification to the traditional primal-dual methods. Leveraging an elaborately constructed weighted error norm sum, it is rigorously proved that the devised algorithm converges to the optimal solution at a linear rate. Finally, numerical simulations are conducted to demonstrate the theoretical results and show the advantages of the proposed algorithm.