Event‐triggered distributed algorithm for searching general Nash equilibrium with general step‐size

2020 ◽  
Author(s):  
Ran Li ◽  
Xiaowu Mu
Keyword(s):  
Nash Equilibrium ◽  
Distributed Algorithm ◽  
Step Size ◽  
Event Triggered ◽  
General Step

Distributed Nash Equilibrium Seeking Under Event-Triggered Mechanism

2021 ◽  
pp. 1-1
Author(s):  
Kaijie Zhang ◽  
Xiao Fang ◽  
Dandan Wang ◽  
Yuezu Lv ◽  
Xinghuo Yu
Keyword(s):  
Nash Equilibrium ◽  
Event Triggered

On the Accelerated Convergence of the Decentralized Event-triggered Algorithm for Convex Optimization

2021 ◽  
Vol 30 (01) ◽  
pp. 2140003
Author(s):  
Keke Zhang ◽  
Jiang Xiong ◽  
Xiangguang Dai
Keyword(s):  
Cost Function ◽  
Optimal Solution ◽  
Linear Convergence ◽  
Step Size ◽  
Undirected Network ◽  
Momentum Coefficient ◽  
Convex Cost ◽  
Local Convex ◽  
The Cost ◽  
Event Triggered

This article considers a problem of solving the optimal solution of the sum of locally convex cost functions over an undirected network. Each local convex cost function in the network is accessed only by each unit. To be able to reduce the amount of computation and get the desired result in an accelerated way, we put forward a fresh accelerated decentralized event-triggered algorithm, named as A-DETA, for the optimization problem. A-DETA combines gradient tracking and two momentum accelerated terms, adopts nonuniform step-sizes and emphasizes that each unit interacts with neighboring units independently only at the sampling time triggered by the event. On the premise of assuming the smoothness and strong convexity of the cost function, it is proved that A-DETA can obtain the exact optimal solution linearly in the event of sufficiently small positive step-size and momentum coefficient. Moreover, an explicit linear convergence speed is definitely shown. Finally, extensive simulation example validates the usability of A-DETA.

Distributed Nash Equilibrium Seeking for Quadratic Games with Security

2019 ◽  
Vol 28 (04) ◽  
pp. 1950009
Author(s):  
Shouwei Zhang ◽  
Shu Liang
Keyword(s):  
Nash Equilibrium ◽  
Lyapunov Function ◽  
Invariance Principle ◽  
Distributed Algorithm ◽  
Differential Inclusions ◽  
Cost Functions ◽  
Quadratic Cost ◽  
Private Data

Considering a game with quadratic cost functions, this paper presents a distributed algorithm with security, whereby each player updates its strategy variable without using its private data and still achieves the Nash equilibrium. By using the theory of differential inclusions, Lyapunov function and invariance principle, the algorithm is proved to be convergent. Our algorithm can be used when it is required to seek the Nash equilibrium without disclosure of private data.

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