  This paper is mainly devoted to the distributed second-order multi-agent
optimization problem with unbalanced and directed networks. To deal with this
problem, a new distributed algorithm is proposed based on the local neighbor
information and the private objective functions. By a coordination
transformation, the closed-loop system is divided into two first-order
subsystems, which is easier to be dealt with. Under the assumption of the
strong connectivity of networks, it is proved that all agent can
collaboratively converge to some optimal solution of the team objective
function, where the gradient of the private objective functions is not assumed
to be bounded.
