A distributed algorithm for solving mixed equilibrium problems. (July 2019) - Lu, Kaihong; Jing, Gangshan; Wang, Long
Abstract: In this paper, the mixed equilibrium problem is solved by a multi-agent network. The objective for agents is to cooperatively find a point in a convex set, at which the sum of some local bifunctions with a free variable is non-negative. To address this problem, we propose a distributed extragradient algorithm based on a consensus strategy. By implementing the algorithm, each agent adjusts its state value by only using its own bifunction information and the local state information received from its immediate neighbors. Under mild conditions on the graph and bifunctions, it is shown that all agents reach agreement asymptotically, and the consensus state is a solution to the equilibrium problem. A simulation example is presented to demonstrate the effectiveness of our theoretical results.