Distributed algorithm for mixed equilibrium problems with event-triggered strategy

A new iterative method based on the event-triggered strategy for finding a solution to a mixed equilibrium problem (MEP) is introduced in this paper. The target of the MEP is to find a point in a closed convex set, guaranteeing that the sum of bifunctions about this point is non-negative. To decrease the cost of communication, the MEP is investigated with an event-triggered protocol. Furthermore, it is the first attempt to combine the MEP with an event-triggered strategy. Although there exist difficulties caused by the asymmetry of the network structure associated with directed graphs, nonlinearity and strong coupling of the MEP, the novel algorithm for directed graphs, two event-triggered conditions and the range of the solution associated with the MEP are obtained to handle these challenges. Under the directed time-varying graph, the designed algorithm can converge to a solution to the MEP and reach average consensus. Finally, a numerical example is presented to illustrate the effectiveness of the above algorithm.