Distributed Algorithm for Nonsmooth Resource Allocation Problems With Nonlinear Constraints and Its Application to Smart Grids

In this article, we study nondifferentiable resource allocation problems (RAPs). In our problem, the decisions of agents are subject to coupling inequality constraints, local inequality constraints, and local convex set constraints. In contrast to existing RAPs, the cost functions are nonsmooth and...

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Published inIEEE systems journal Vol. 17; no. 2; pp. 1 - 10
Main Authors Deng, Zhenhua, Chen, Tao, Zhao, Yan
Format Journal Article
LanguageEnglish
Published New York IEEE 01.06.2023
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Algorithms
Computational geometry
Convergence
Convexity
Cost function
Costs
Distributed algorithms
Graph theory
Inclusions
multiagent systems
nonlinear constraints
nonsmooth analysis
Optimization
Power dispatch
Resource allocation
Resource management
Smart grid
Smart grids
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Abstract In this article, we study nondifferentiable resource allocation problems (RAPs). In our problem, the decisions of agents are subject to coupling inequality constraints, local inequality constraints, and local convex set constraints. In contrast to existing RAPs, the cost functions are nonsmooth and the inequality constraints are nonsmooth and nonlinear in our problem. Based on differential inclusions and projection methods, we exploit a fully distributed subgradient-based resource allocation algorithm to optimally allocate the network resources. With the help of the set-valued LaSalle invariance principle, we prove the global convergence of the algorithm to the optimal resource allocation of our problem. Finally, our method is applied to the economic dispatch problems of smart grids. With our method, the generations of generating units converge to the optimal power generation.
AbstractList In this article, we study nondifferentiable resource allocation problems (RAPs). In our problem, the decisions of agents are subject to coupling inequality constraints, local inequality constraints, and local convex set constraints. In contrast to existing RAPs, the cost functions are nonsmooth and the inequality constraints are nonsmooth and nonlinear in our problem. Based on differential inclusions and projection methods, we exploit a fully distributed subgradient-based resource allocation algorithm to optimally allocate the network resources. With the help of the set-valued LaSalle invariance principle, we prove the global convergence of the algorithm to the optimal resource allocation of our problem. Finally, our method is applied to the economic dispatch problems of smart grids. With our method, the generations of generating units converge to the optimal power generation.
Author Chen, Tao
Zhao, Yan
Deng, Zhenhua
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Snippet In this article, we study nondifferentiable resource allocation problems (RAPs). In our problem, the decisions of agents are subject to coupling inequality...
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SubjectTerms Algorithms
Computational geometry
Convergence
Convexity
Cost function
Costs
Distributed algorithms
Graph theory
Inclusions
multiagent systems
nonlinear constraints
nonsmooth analysis
Optimization
Power dispatch
Resource allocation
Resource management
Smart grid
Smart grids
Title Distributed Algorithm for Nonsmooth Resource Allocation Problems With Nonlinear Constraints and Its Application to Smart Grids
URI https://ieeexplore.ieee.org/document/9998477
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Volume 17
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