Abstract
This chapter proposes a parallel computing framework to distributedly solve robust convex optimization (RCO) when the constraints are affected by nonlinear uncertainty. To this end, we adopt a scenario approach by randomly sampling the uncertainty set. However, the number of samples to attain high levels of probabilistic guarantee of robustness may be large, which results in a large number of constraints in the scenario problem (SP). Instead of using a single processor, we resort to many processors that are distributed among different nodes of time-varying unbalanced digraphs. Then, we propose a random projected algorithm solve the SP, which is given in an explicitly recursive form with simple iteration. We show that if the sequence of digraphs are uniformly jointly strongly connected (UJSC), each node asymptotically converges to a common optimal solution to the SP. That is, the RCO is effectively solved in a distributed parallel way.
Portions of this chapter were previously presented at the 2016 ACC and the material is used with permission of the AACC. (Keyou You, Roberto Tempo, “Parallel algorithms for robust convex programs over networks”, in Proceedings of the 2016 American Control Conference, https://doi.org/10.1109/ACC.2016.7525215)
R. Tempo—Author deceased.
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Acknowledgements
This work was supported by the National Natural Science Foundation of China (41576101), Tsinghua University Initiative Scientific Research Program, and CNR International Joint Lab COOPS.
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You, K., Tempo, R. (2018). Networked Parallel Algorithms for Robust Convex Optimization via the Scenario Approach. In: Tempo, R., Yurkovich, S., Misra, P. (eds) Emerging Applications of Control and Systems Theory. Lecture Notes in Control and Information Sciences - Proceedings. Springer, Cham. https://doi.org/10.1007/978-3-319-67068-3_25
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