  This paper considers distributed optimization for minimizing the average of
local nonconvex cost functions, by using local information exchange over
undirected communication networks. To reduce the required communication
capacity, we introduce an encoder--decoder scheme. By integrating them with
distributed gradient tracking and proportional integral algorithms,
respectively, we then propose two quantized distributed nonconvex optimization
algorithms. Assuming the global cost function satisfies the
Polyak--{\L}ojasiewicz condition, which does not require the global cost
function to be convex and the global minimizer is not necessarily unique, we
show that our proposed algorithms linearly converge to a global optimal point
and that larger quantization level leads to faster convergence speed. Moreover,
we show that a low data rate is sufficient to guarantee linear convergence when
the algorithm parameters are properly chosen. The theoretical results are
illustrated by numerical examples.
