  This paper proposes a distributed dual gradient tracking algorithm (DDGT) to
solve resource allocation problems over an unbalanced network, where each node
in the network holds a private cost function and computes the optimal resource
by interacting only with its neighboring nodes. Our key idea is the novel use
of the distributed push-pull gradient algorithm (PPG) to solve the dual problem
of the resource allocation problem. To study the convergence of the DDGT, we
first establish the sublinear convergence rate of PPG for non-convex objective
functions, which advances the existing results on PPG as they require the
strong-convexity of objective functions. Then we show that the DDGT converges
linearly for strongly convex and Lipschitz smooth cost functions, and
sublinearly without the Lipschitz smoothness. Finally, experimental results
suggest that DDGT outperforms existing algorithms.
