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

Quantized Distributed Nonconvex Optimization Algorithms with Linear Convergence under the Polyak--${\L}$ojasiewicz Condition