In this paper, we focus on an aggregative optimization problem under the communication bottleneck. The aggregative optimization is to minimize the sum of local cost functions. Each cost function depends on not only local state variables but also the sum of functions of global state variables. The goal is to solve the aggregative optimization problem through distributed computation and local efficient communication over a network of agents without a central coordinator. Using the variable tracking...

This paper investigates a distributed algorithm for the multi-agent constrained optimization problem, which is to minimize a global objective function formed by a sum of local convex (possibly nonsmooth) functions under both coupled inequality and affine equality constraints. By introducing auxiliary variables, we decouple the constraints and transform the multi-agent optimization problem into a variational inequality problem with a set-valued monotone mapping. We propose a distributed dual averaging...

Nash equilibrium is recognized as an important solution concept in non-cooperative game theory due to its broad applicability to economics, social sciences, computer science, and engineering. In view of its importance, substantial progress has been made to seek a static Nash equilibrium using distributed methods. However, these approaches are inapplicable in dynamic environments because, in this setting, the Nash equilibrium constantly changes over time. In this paper, we propose a dynamic algorithm...

Distributed optimization over unbalanced graphs is an important problem in multi-agent systems. Most of literatures, by introducing some auxiliary variables, utilize the Push-Sum scheme to handle the widespread unbalance graph with row or column stochastic matrix only. But the introduced auxiliary dynamics bring more calculation and communication tasks. In this paper, based on the in-degree and out-degree information of each agent, we propose an innovative distributed optimization algorithm to reduce...

This paper studies distributed optimization problems of a class of agents with fractional order dynamics and unknown external disturbances. Motivated by the celebrated active disturbance rejection control (ADRC) method, a fractional order extended state observer (Frac-ESO) is first constructed, and an ADRC-based PI-like protocol is then proposed for the target distributed optimization problem. It is rigorously shown that the decision variables of the agents reach a domain of the optimal solution...