A novel computation-efficient quantized distributed optimization algorithm is presented in this article for solving a class of convex optimization problems over time-varying undirected networks with limited communication capacity. These convex optimization problems are usually relevant to the minimization of a sum of local convex objective functions using only local communication and local computation. In most of the existing distributed optimization algorithms, each agent needs to calculate the subgradient of its local convex objective function at each time step, which leads to extremely heavy computation. The proposed algorithm incorporates random sleep scheme into procedures of agents' updates in a probabilistic form to reduce the computation load, and further allows for uncoordinated step-sizes of all agents. The quantized strategy is also applied, which overcomes the limitation of communication capacity. Theoretical analysis indicates that the convex optimization problems can be solved and numerical analysis shows that the computation load of subgradient can be significantly reduced by the proposed algorithm. The boundedness of the quantization levels at each time step has been explicitly characterized. Simulation examples are presented to demonstrate the effectiveness of the algorithm and the correctness of the theoretical results.

中文翻译：

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有限带宽通信的时变网络上凸优化算法的高效计算分布式算法

本文提出一种新颖的计算有效的量化分布式优化算法，用于解决通信容量有限的时变无向网络上的一类凸优化问题。这些凸优化问题通常与仅使用局部通信和局部计算来最小化局部凸目标函数之和有关。在大多数现有的分布式优化算法中，每个代理都需要在每个时间步长计算其局部凸目标函数的子梯度，这会导致计算量极大。所提出的算法以概率形式将随机睡眠方案合并到代理的更新过程中以减少计算负荷，并且进一步允许所有代理的步长不协调。还应用了量化策略，克服了通信容量的限制。理论分析表明，该算法可以解决凸优化问题，数值分析表明，该算法可以显着降低次梯度的计算量。每个时间步长的量化水平的有界性已得到明确表征。仿真算例表明了算法的有效性和理论结果的正确性。每个时间步长的量化水平的有界性已得到明确表征。仿真算例表明了算法的有效性和理论结果的正确性。每个时间步长的量化水平的有界性已得到明确表征。仿真算例表明了算法的有效性和理论结果的正确性。