Projected Primal-Dual Dynamics for Distributed Constrained Nonsmooth Convex Optimization

A distributed nonsmooth convex optimization problem subject to a general type of constraint, including equality and inequality as well as bounded constraints, is studied in this paper for a multiagent network with a fixed and connected communication topology. To collectively solve such a complex opt...

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Published inIEEE transactions on cybernetics Vol. 50; no. 4; pp. 1776 - 1782
Main Authors Zhu, Yanan, Yu, Wenwu, Wen, Guanghui, Chen, Guanrong
Format Journal Article
LanguageEnglish
Published United States IEEE 01.04.2020
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Constraints
Convergence
Convex analysis
Convex functions
Convexity
Cybernetics
Distributed convex optimization
Dynamic stability
Dynamics
Heuristic algorithms
Indexes
Linear programming
multiagent networks
Multiagent systems
nonsmooth analysis
Optimization
primal–dual dynamics
Stability analysis
Topology
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Abstract A distributed nonsmooth convex optimization problem subject to a general type of constraint, including equality and inequality as well as bounded constraints, is studied in this paper for a multiagent network with a fixed and connected communication topology. To collectively solve such a complex optimization problem, primal-dual dynamics with projection operation are investigated under optimal conditions. For the nonsmooth convex optimization problem, a framework under the LaSalle's invariance principle from nonsmooth analysis is established, where the asymptotic stability of the primal-dual dynamics at an optimal solution is guaranteed. For the case where inequality and bounded constraints are not involved and the objective function is twice differentiable and strongly convex, the globally exponential convergence of the primal- dual dynamics is established. Finally, two simulations are provided to verify and visualize the theoretical results.
AbstractList A distributed nonsmooth convex optimization problem subject to a general type of constraint, including equality and inequality as well as bounded constraints, is studied in this paper for a multiagent network with a fixed and connected communication topology. To collectively solve such a complex optimization problem, primal-dual dynamics with projection operation are investigated under optimal conditions. For the nonsmooth convex optimization problem, a framework under the LaSalle's invariance principle from nonsmooth analysis is established, where the asymptotic stability of the primal-dual dynamics at an optimal solution is guaranteed. For the case where inequality and bounded constraints are not involved and the objective function is twice differentiable and strongly convex, the globally exponential convergence of the primal-dual dynamics is established. Finally, two simulations are provided to verify and visualize the theoretical results.A distributed nonsmooth convex optimization problem subject to a general type of constraint, including equality and inequality as well as bounded constraints, is studied in this paper for a multiagent network with a fixed and connected communication topology. To collectively solve such a complex optimization problem, primal-dual dynamics with projection operation are investigated under optimal conditions. For the nonsmooth convex optimization problem, a framework under the LaSalle's invariance principle from nonsmooth analysis is established, where the asymptotic stability of the primal-dual dynamics at an optimal solution is guaranteed. For the case where inequality and bounded constraints are not involved and the objective function is twice differentiable and strongly convex, the globally exponential convergence of the primal-dual dynamics is established. Finally, two simulations are provided to verify and visualize the theoretical results.
A distributed nonsmooth convex optimization problem subject to a general type of constraint, including equality and inequality as well as bounded constraints, is studied in this paper for a multiagent network with a fixed and connected communication topology. To collectively solve such a complex optimization problem, primal–dual dynamics with projection operation are investigated under optimal conditions. For the nonsmooth convex optimization problem, a framework under the LaSalle’s invariance principle from nonsmooth analysis is established, where the asymptotic stability of the primal–dual dynamics at an optimal solution is guaranteed. For the case where inequality and bounded constraints are not involved and the objective function is twice differentiable and strongly convex, the globally exponential convergence of the primal–dual dynamics is established. Finally, two simulations are provided to verify and visualize the theoretical results.
Author Zhu, Yanan
Yu, Wenwu
Wen, Guanghui
Chen, Guanrong
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Snippet A distributed nonsmooth convex optimization problem subject to a general type of constraint, including equality and inequality as well as bounded constraints,...
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SubjectTerms Constraints
Convergence
Convex analysis
Convex functions
Convexity
Cybernetics
Distributed convex optimization
Dynamic stability
Dynamics
Heuristic algorithms
Indexes
Linear programming
multiagent networks
Multiagent systems
nonsmooth analysis
Optimization
primal–dual dynamics
Stability analysis
Topology
Title Projected Primal-Dual Dynamics for Distributed Constrained Nonsmooth Convex Optimization
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