Abstract
This paper studies a distributed robust resource allocation problem with nonsmooth objective functions under polyhedral uncertain allocation parameters. In the considered distributed robust resource allocation problem, the (nonsmooth) objective function is a sum of local convex objective functions assigned to agents in a multi-agent network. Each agent has a private feasible set and decides a local variable, and all the local variables are coupled with a global affine inequality constraint, which is subject to polyhedral uncertain parameters. With the duality theory of convex optimization, the authors derive a robust counterpart of the robust resource allocation problem. Based on the robust counterpart, the authors propose a novel distributed continuous-time algorithm, in which each agent only knows its local objective function, local uncertainty parameter, local constraint set, and its neighbors’ information. Using the stability theory of differential inclusions, the authors show that the algorithm is able to find the optimal solution under some mild conditions. Finally, the authors give an example to illustrate the efficacy of the proposed algorithm.
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This research was supported by the National Key Research and Development Program of China under Grant No. 2016YFB0901902, the National Natural Science Foundation of China under Grant Nos. 61573344, 61603378, 61621063, and 61781340258, Beijing Natural Science Foundation under Grant No. 4152057, Projects of Major International (Regional) Joint Research Program NSFC under Grant No. 61720106011.
This paper was recommended for publication by Guest Editor XIN Bin.
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Zeng, X., Yi, P. & Hong, Y. Distributed Algorithm for Robust Resource Allocation with Polyhedral Uncertain Allocation Parameters. J Syst Sci Complex 31, 103–119 (2018). https://doi.org/10.1007/s11424-018-7145-5
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DOI: https://doi.org/10.1007/s11424-018-7145-5