# A Primal Decomposition Approach to Globally Coupled Aggregative Optimization over Networks

@article{Huang2021APD, title={A Primal Decomposition Approach to Globally Coupled Aggregative Optimization over Networks}, author={Yuanhanqing Huang and Jianghai Hu}, journal={ArXiv}, year={2021}, volume={abs/2109.12297} }

We consider a class of multi-agent 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 theβ¦Β Expand

#### References

SHOWING 1-10 OF 31 REFERENCES

Dual decomposition for multi-agent distributed optimization with coupling constraints

- Mathematics, Computer Science
- Autom.
- 2017

This work proposes a novel distributed algorithm to minimize the sum of the agentsβ objective functions subject to both local and coupling constraints, where dual decomposition and proximal minimization are combined in an iterative scheme. Expand

Distributed Constraint-Coupled Optimization via Primal Decomposition over Random Time-Varying Graphs

- Computer Science, Mathematics
- Autom.
- 2021

This paper proposes a novel distributed algorithm in which agents negotiate a local allocation of the total resource only with neighbors with active communication links, and shows almost sure convergence to the optimal cost of the original problem and almost sure asymptotic primal recovery without resorting to averaging mechanisms typically employed in dual decomposition schemes. Expand

Distributed Algorithms for Solving Locally Coupled Optimization Problems on Agent Networks

- Computer Science
- 2018 IEEE Conference on Decision and Control (CDC)
- 2018

Several algorithms are proposed based on operator splitting techniques that can iteratively converge to an optimal primal (or dual) solution of the optimization problems for a group of agents whose individual objective functions and constraints may depend on the variables of neighboring agents. Expand

An operator splitting approach for distributed generalized Nash equilibria computation

- Computer Science, Mathematics
- Autom.
- 2019

A distributed algorithm for computation of a generalized Nash equilibrium (GNE) in noncooperative games over networks in which the feasible decision sets of all players are coupled together by a globally shared affine constraint is proposed. Expand

LANA: An ADMM-like Nash equilibrium seeking algorithm in decentralized environment

- Mathematics, Computer Science
- 2017 American Control Conference (ACC)
- 2017

A linearized alternating direction method of multipliers-like Nash equilibrium seeking algorithm (LANA) for a class of non-cooperative games over generally connected networks that involves every player performing gradient play to minimize his own objective selfishly while sharing, retrieving, and combining information locally among his network neighborhood. Expand

Distributed convergence to Nash equilibria in network and average aggregative games

- Computer Science
- Autom.
- 2020

A class of distributed algorithms that can be used to steer the strategies of the rational agents to a Nash equilibrium configuration, with guaranteed convergence under different sufficient conditions depending on the cost functions and on the network is proposed. Expand

Distributed GNE Seeking Under Partial-Decision Information Over Networks via a Doubly-Augmented Operator Splitting Approach

- Computer Science, Mathematics
- IEEE Transactions on Automatic Control
- 2020

A single-layer algorithm is introduced, fully distributed with respect to both primal and dual variables, and its convergence to a variational GNE with fixed step sizes is shown, by reformulating it as a forwardβbackward iteration for a pair of doubly-augmented monotone operators. Expand

Distributed Nash equilibrium seeking for aggregative games with coupled constraints

- Computer Science, Mathematics
- Autom.
- 2017

The convergence of the non-smooth algorithm for the distributed game is proved by taking advantage of its special structure and also combining the techniques of the variational inequality and Lyapunov function. Expand

A survey of distributed optimization

- Computer Science
- Annu. Rev. Control.
- 2019

This survey paper aims to offer a detailed overview of existing distributed optimization algorithms and their applications in power systems, and focuses on the application of distributed optimization in the optimal coordination of distributed energy resources. Expand

A Distributed Algorithm For Almost-Nash Equilibria of Average Aggregative Games With Coupling Constraints

- Computer Science
- IEEE Transactions on Control of Network Systems
- 2020

A distributed algorithm is proposed that achieves an $\varepsilon$-Nash equilibrium by requiring only local communications of the agents, as specified by a sparse communication network. Expand