  We propose two distributed iterative algorithms that can be used to solve, in
finite time, the distributed optimization problem over quadratic local cost
functions in large-scale networks. The first algorithm exhibits synchronous
operation whereas the second one exhibits asynchronous operation. Both
algorithms share salient features. Specifically, the algorithms operate
exclusively with quantized values, which means that the information stored,
processed and exchanged between neighboring nodes is subject to deterministic
uniform quantization. The algorithms rely on event-driven updates in order to
reduce energy consumption, communication bandwidth, network congestion, and/or
processor usage. Finally, once the algorithms converge, nodes distributively
terminate their operation. We prove that our algorithms converge in a finite
number of iterations to the exact optimal solution depending on the
quantization level, and we present applications of our algorithms to (i)
optimal task scheduling for data centers, and (ii) global model aggregation for
distributed federated learning. We provide simulations of these applications to
illustrate the operation, performance, and advantages of the proposed
algorithms. Additionally, it is shown that our proposed algorithms compare
favorably to algorithms in the current literature. Quantized communication and
asynchronous updates increase the required time to completion, but finite-time
operation is maintained.
