Distributed Algorithm for Robust Resource Allocation with Polyhedral Uncertain Allocation Parameters
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 a...
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| Veröffentlicht in: | Journal of systems science and complexity Jg. 31; H. 1; S. 103 - 119 |
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| Sprache: | Englisch |
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Beijing
Academy of Mathematics and Systems Science, Chinese Academy of Sciences
01.02.2018
Springer Nature B.V |
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| ISSN: | 1009-6124, 1559-7067 |
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| 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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| AbstractList | 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. |
| Author | Hong, Yiguang Yi, Peng Zeng, Xianlin |
| Author_xml | – sequence: 1 givenname: Xianlin surname: Zeng fullname: Zeng, Xianlin email: xianlin.zeng@bit.edu.cn organization: School of Automation, Beijing Institute of Technology – sequence: 2 givenname: Peng surname: Yi fullname: Yi, Peng organization: Department of Electrical and Systems Engineering, Washington University in St. Louis – sequence: 3 givenname: Yiguang surname: Hong fullname: Hong, Yiguang organization: Key Laboratory of Systems and Control, Institute of Systems Science, Chinese Academy of Sciences |
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| Keywords | polyhedral uncertain parameters Distributed optimization resource allocation nonsmooth optimization robust optimization |
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| SubjectTerms | Algorithms Complex Systems Computational geometry Control Convexity Economic models Mathematics Mathematics and Statistics Mathematics of Computing Multiagent systems Operations Research/Decision Theory Optimization Optimization algorithms Parameter uncertainty Resource allocation Robustness Statistics Systems Theory |
| Title | Distributed Algorithm for Robust Resource Allocation with Polyhedral Uncertain Allocation Parameters |
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