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Distributed optimization is ubiquitous in emerging applications, such as robust sensor network control, smart grid management, machine learning, resource slicing, and localization. However, the extensive data exchange among local and central nodes may cause a severe communication bottleneck. To overcome this challenge, over-the-air computing (AirComp) is a promising medium access technology, which exploits the superposition property of the wireless multiple access channel (MAC) and offers significant bandwidth savings. In this work, we propose an AirComp framework for general distributed convex optimization problems. Specifically, a distributed primal-dual (DPD) subgradient method is utilized for the optimization procedure. Under general assumptions, we prove that DPD-AirComp can asymptotically achieve zero expected constraint violation. Therefore, DPD-AirComp ensures the feasibility of the …