Federated learning has shown its advances over the last few years but is
facing many challenges, such as how algorithms save communication resources,
how they reduce computational costs, and whether they converge. To address
these issues, this paper proposes a new federated learning algorithm (FedGiA)
that combines the gradient descent and the inexact alternating direction method
of multipliers. It is shown that FedGiA is computation and
communication-efficient and convergent linearly under mild conditions.