Online distributed optimization with strongly pseudoconvex-sum cost functions and coupled inequality constraints

In this paper, the problem of online distributed optimization with coupled inequality constraints is studied by employing multi-agent systems. Each agent only has access to the information associated with its own cost function and a local block of the constraint function, and can exchange local information with its immediate neighbors via a time-varying digraph. Moreover, the information of current cost functions and constraint functions is not available to agents until decisions are made. Of particular interest is that the cost function is considered to be strongly pseudoconvex. To handle this problem, an auxiliary optimization-based online distributed primal-dual algorithm is proposed. The performance of the algorithm is measured by the dynamic regret and the constraint violation. Under mild assumptions on graphs, we prove that if the cumulative deviation of minimizer sequence grows within a certain rate, then both the dynamic regret and the violation of coupled inequality constraints grow sublinearly. Finally, a simulation example is given to corroborate the validity of our results. & COPY; 2023 Elsevier Ltd. All rights reserved.