Distributed Discrete-Time Convex Optimization With Closed Convex Set Constraints: Linearly Convergent Algorithm Design

The convergence rate and applicability to directed graphs with interaction topologies are two important features for practical applications of distributed optimization algorithms. In this article, a new kind of fast distributed discrete-time algorithms is developed for solving convex optimization pr...

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Veröffentlicht in:	IEEE transactions on cybernetics Jg. 54; H. 4; S. 2271 - 2283
Hauptverfasser:	Luan, Meng, Wen, Guanghui, Liu, Hongzhe, Huang, Tingwen, Chen, Guanrong, Yu, Wenwu
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	United States IEEE 01.04.2024 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:	Algorithms Computational geometry Consensus Consensus algorithm Convergence Convex functions Convexity directed interaction topology distributed constrained optimization Eigenvalues and eigenfunctions gradient tracking Graph theory Graphs linear convergence rate Momentum Network topology Numerical simulation Optimization Topology
ISSN:	2168-2267, 2168-2275, 2168-2275
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Abstract	The convergence rate and applicability to directed graphs with interaction topologies are two important features for practical applications of distributed optimization algorithms. In this article, a new kind of fast distributed discrete-time algorithms is developed for solving convex optimization problems with closed convex set constraints over directed interaction networks. Under the gradient tracking framework, two distributed algorithms are, respectively, designed over balanced and unbalanced graphs, where momentum terms and two time-scales are involved. Furthermore, it is demonstrated that the designed distributed algorithms attain linear speedup convergence rates provided that the momentum coefficients and the step size are appropriately selected. Finally, numerical simulations verify the effectiveness and the global accelerated effect of the designed algorithms.
AbstractList	The convergence rate and applicability to directed graphs with interaction topologies are two important features for practical applications of distributed optimization algorithms. In this article, a new kind of fast distributed discrete-time algorithms is developed for solving convex optimization problems with closed convex set constraints over directed interaction networks. Under the gradient tracking framework, two distributed algorithms are, respectively, designed over balanced and unbalanced graphs, where momentum terms and two time-scales are involved. Furthermore, it is demonstrated that the designed distributed algorithms attain linear speedup convergence rates provided that the momentum coefficients and the step size are appropriately selected. Finally, numerical simulations verify the effectiveness and the global accelerated effect of the designed algorithms.The convergence rate and applicability to directed graphs with interaction topologies are two important features for practical applications of distributed optimization algorithms. In this article, a new kind of fast distributed discrete-time algorithms is developed for solving convex optimization problems with closed convex set constraints over directed interaction networks. Under the gradient tracking framework, two distributed algorithms are, respectively, designed over balanced and unbalanced graphs, where momentum terms and two time-scales are involved. Furthermore, it is demonstrated that the designed distributed algorithms attain linear speedup convergence rates provided that the momentum coefficients and the step size are appropriately selected. Finally, numerical simulations verify the effectiveness and the global accelerated effect of the designed algorithms. The convergence rate and applicability to directed graphs with interaction topologies are two important features for practical applications of distributed optimization algorithms. In this article, a new kind of fast distributed discrete-time algorithms is developed for solving convex optimization problems with closed convex set constraints over directed interaction networks. Under the gradient tracking framework, two distributed algorithms are, respectively, designed over balanced and unbalanced graphs, where momentum terms and two time-scales are involved. Furthermore, it is demonstrated that the designed distributed algorithms attain linear speedup convergence rates provided that the momentum coefficients and the step size are appropriately selected. Finally, numerical simulations verify the effectiveness and the global accelerated effect of the designed algorithms.
Author	Huang, Tingwen Luan, Meng Wen, Guanghui Yu, Wenwu Liu, Hongzhe Chen, Guanrong
Author_xml	– sequence: 1 givenname: Meng surname: Luan fullname: Luan, Meng email: 230228433@seu.edu.cn organization: Department of Systems Science, School of Mathematics, Southeast University, Nanjing, China – sequence: 2 givenname: Guanghui orcidid: 0000-0003-0070-8597 surname: Wen fullname: Wen, Guanghui email: wenguanghui@gmail.com organization: Department of Systems Science, School of Mathematics, Southeast University, Nanjing, China – sequence: 3 givenname: Hongzhe orcidid: 0000-0002-6887-368X surname: Liu fullname: Liu, Hongzhe email: 101300130@seu.edu.cn organization: Department of Systems Science, School of Mathematics, Southeast University, Nanjing, China – sequence: 4 givenname: Tingwen orcidid: 0000-0001-9610-846X surname: Huang fullname: Huang, Tingwen email: tingwen.huang@qatar.tamu.edu organization: Department of Science, Texas A&M University at Qatar, Doha, Qatar – sequence: 5 givenname: Guanrong orcidid: 0000-0003-1381-7418 surname: Chen fullname: Chen, Guanrong email: eegchen@cityu.edu.hk organization: Department of Electrical Engineering, City University of Hong Kong, Hong Kong, China – sequence: 6 givenname: Wenwu orcidid: 0000-0001-6406-2399 surname: Yu fullname: Yu, Wenwu email: wwyu@seu.edu.cn organization: Department of Systems Science, School of Mathematics, Southeast University, Nanjing, China
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SubjectTerms	Algorithms Computational geometry Consensus Consensus algorithm Convergence Convex functions Convexity directed interaction topology distributed constrained optimization Eigenvalues and eigenfunctions gradient tracking Graph theory Graphs linear convergence rate Momentum Network topology Numerical simulation Optimization Topology
Title	Distributed Discrete-Time Convex Optimization With Closed Convex Set Constraints: Linearly Convergent Algorithm Design
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