Journal
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
Volume 67, Issue 6, Pages 3029-3035Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2021.3091096
Keywords
Optimization; Linear programming; Distributed algorithms; Convex functions; Mirrors; Standards; Mathematical model; Distributed nonconvex optimization; multiagent systems (MASs); online optimization
Funding
- National Natural Science Foundation of China [NSFC 62036002]
- China Postdoctoral Science Foundation [2021M691313]
- PKU-Baidu Fund [2020BD017]
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In this article, the problem of online distributed optimization with a set constraint is solved using a network of agents. An online distributed algorithm based on the consensus algorithm and the mirror descent algorithm is proposed to handle nonconvex objective functions. Under mild assumptions on the communication graph and objective functions, the algorithm's performance is proven.
In this article, the problem of online distributed optimization with a set constraint is solved by employing a network of agents. Each agent only has access to a local objective function and set constraint, and can only communicate with its neighbors via a digraph, which is not necessarily balanced. Moreover, agents do not have prior knowledge of their future objective functions. Different from existing works on online distributed optimization, we consider the scenario, where objective functions at each time step are nonconvex. To handle this challenge, we propose an online distributed algorithm based on the consensus algorithm and the mirror descent algorithm. Of particular interest is that regrets involving first-order optimality condition are used to measure the performance of the proposed algorithm. Under mild assumptions on the communication graph and objective functions, we prove that regrets grow sublinearly. Finally, a simulation example is worked out to demonstrate the effectiveness of our theoretical results.
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