Geodesic
Distributed optimization with inexact oracle
Kybernetika, Tome 58 (2022) no. 4, pp. 578-592.

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In this paper, we study the distributed optimization problem using approximate first-order information. We suppose the agent can repeatedly call an inexact first-order oracle of each individual objective function and exchange information with its time-varying neighbors. We revisit the distributed subgradient method in this circumstance and show its suboptimality under square summable but not summable step sizes. We also present several conditions on the inexactness of the local oracles to ensure an exact convergence of the iterative sequences towards the global optimal solution. A numerical example is given to verify the efficiency of our algorithm.
DOI : 10.14736/kyb-2022-4-0578
Classification : 65K10, 93A16
Keywords: distributed optimization; inexact oracle; first-order method; multi-agent network; time-varying topology 
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Zhu, Kui; Zhang, Yichen; Tang, Yutao. Distributed optimization with inexact oracle. Kybernetika, Tome 58 (2022) no. 4, pp. 578-592. doi : 10.14736/kyb-2022-4-0578. http://geodesic.mathdoc.fr/articles/10.14736/kyb-2022-4-0578/

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