  This paper focuses on the decentralized optimization problem, where agents in
a network cooperate to minimize the sum of their local objective functions by
information exchange and local computation. Based on the alternating direction
method of multipliers (ADMM), we propose CC-DQM, a communication-efficient
decentralized second-order optimization algorithm that combines compressed
communication with event-triggered communication. Specifically, agents are
allowed to transmit the compressed message only when the current primal
variables have changed greatly compared to its last estimate. Moreover, to
relieve the computation cost, the update of Hessian is scheduled by the trigger
condition. To maintain exact linear convergence under compression, we compress
the difference between the information to be transmitted and its estimate by a
general contractive compressor. Theoretical analysis shows that CC-DQM can
still achieve an exact linear convergence, despite the existence of compression
error and intermittent communication, if the objective functions are strongly
convex and smooth. Finally, we validate the performance of CC-DQM by numerical
experiments.
