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This paper addresses the problem of distributed optimization, where a networkof agents represented as a directed graph (digraph) aims to collaborativelyminimize the sum of their individual cost functions. Existing approaches fordistributed optimization over digraphs, such as Push-Pull, require agents toexchange explicit state values with their neighbors in order to reach anoptimal solution. However, this can result in the disclosure of sensitive andprivate information. To overcome this issue, we propose astate-decomposition-based privacy-preserving finite-time push-sum (PrFTPS)algorithm without any global information, such as network size or graphdiameter. Then, based on PrFTPS, we design a gradient descent algorithm(PrFTPS-GD) to solve the distributed optimization problem. It is proved thatunder PrFTPS-GD, the privacy of each agent is preserved and the linearconvergence rate related to the optimization iteration number is achieved.Finally, numerical simulations are provided to illustrate the effectiveness ofthe proposed approach.

A Privacy-Preserving Finite-Time Push-Sum based Gradient Method for Distributed Optimization over Digraphs