Distributed Projection Algorithm for Solving Variational Inequalities

In this paper, we study a distributed computation model to solve a system of variational inequalities corresponding to multiple agents. Each agent knows a part of the full mapping and is allowed to communicate with its neighbors through a time-varying communication network. To solve this problem, we propose a consensus-based distributed projection gradient algorithm relying on local computation and communication at each agent. We show that this algorithm is able to generate an approximate solution to these variational inequalities under mild assumptions.