Convex Optimization And Game Problem Of Distributed Event-Triggered Algorithm With General Step Size

With the emergence of complex systems and large-scale networks,multiagent systems have received extensive attention in the fields of biology,economy,and engineering.Individuals which can autonomously make decisions are regarded as agents.Systems where agents communicate with each other and work together through coordination are called multiagent systems.In practical engineering,most of the multiagent systems which use distributed networks to solve problems can be transformed into optimization problems.Through distributed networks,agents in the system transmit and exchange information.Owing to continual communication among agents increases the communication burden and causes unnecessary resource consumption,this paper introduces event-trigger mechanism in algorithm design to alleviate this problem.In the algorithm design of system update,the selection of step size can affect the convergence of the system.In the design of the distributed algorithm for convex optimization problem and game problem of a multiagent system,the step-size,required higher condition,is usually designed under the condition of square summable.Therefore,this paper focuses on the general step size which is square non-summable.Introducing the ergodic average sequence,we solve the convergence problem which is caused by the step size of square non-summable.This paper mainly studies the convex optimization problem and the generalized Nash equilibrium problem under the event-triggered algorithm with general step size.Firstly,in the time-varying directed switching topology,consistency and optimality of the discrete-time system can be achieved by using the algorithm with the general step size under bounded constraints.Secondly,under the constraints of bounded,coupled equality and private inequality,the generalized Nash equilibrium can still be found in the continuous-time system by introducing the event triggering algorithm and weakening the step size,and zeno phenomenon does not exist in the system.Finally,the effectiveness of the design algorithm and the correctness of the theoretical results are verified by the simulation examples.