  Federated learning has shown its advances recently but is still facing many
challenges, such as how algorithms save communication resources and reduce
computational costs, and whether they converge. To address these critical
issues, we propose a hybrid federated learning algorithm (FedGiA) that combines
the gradient descent and the inexact alternating direction method of
multipliers. The proposed algorithm is more communication- and
computation-efficient than several state-of-the-art algorithms theoretically
and numerically. Moreover, it also converges globally under mild conditions.
