Distributed optimization increasingly plays a central role in economical and sustainable operation of cyber-physical systems. Nevertheless, the complete potential of the technology has not yet been fully exploited in practice due to communication limitations posed by the real-world infrastructures. Our work investigates fundamental properties of dual gradient methods in distributed resource allocation optimization, where the gradient information is communicated using a limited number of bits. Sufficient and necessary conditions are provided on the quantization set to guarantee the optimality and convergence of the algorithms. We also investigate communication complexity of the problem, the minimal number of communicated bits needed to solve some classes of resource allocation problems regardless of the used algorithms.

This is the joint work with Sindri Magnusson, Chinwendu Enyioha, Carlo Fischione, and Vahid Tarokh.