Distributed algorithms for solving convex inequalities

Abstract: In this paper, a distributed subgradient-based algorithm is proposed for continuous-time multi-agent systems to search a feasible solution to convex inequalities. The algorithm involves each agent achieving a state constrained by its own inequalities while exchanging local information with other agents under a time-varying directed communication graph. With the validity of a mild connectivity condition associated with the communication graph, it is shown that all agents will reach agreement asymptotically and the consensus state is in the solution set of the inequalities. Furthermore, the method is also extended to solving the distributed optimization problem of minimizing the sum of local objective functions subject to convex inequalities. A simulation example is presented to demonstrate the effectiveness of the theoretical results.