  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.
