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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Bibliographic Details
Published in:Journal of systems science and complexity Vol. 31; no. 1; pp. 103 - 119
Main Authors: Zeng, Xianlin, Yi, Peng, Hong, Yiguang
Format: Journal Article
Language:English
Published: Beijing Academy of Mathematics and Systems Science, Chinese Academy of Sciences 01.02.2018
Springer Nature B.V
Subjects:
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
polyhedral uncertain parameters
Distributed optimization
resource allocation
nonsmooth optimization
robust optimization
ISSN:1009-6124, 1559-7067
Online Access:Get full text
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Summary: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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ISSN:1009-6124
1559-7067
DOI:10.1007/s11424-018-7145-5