Penalty Dual Decomposition Method for Nonsmooth Nonconvex Optimization-Part II: Applications

In Part I of this paper, we proposed and analyzed a novel algorithmic framework, termed penalty dual decomposition (PDD), for the minimization of a nonconvex nonsmooth objective function, subject to difficult coupling constraints. Part II of this paper is devoted to evaluation of the proposed method...

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Vydáno v:	IEEE transactions on signal processing Ročník 68; s. 4242 - 4257
Hlavní autoři:	Shi, Qingjiang, Hong, Mingyi, Fu, Xiao, Chang, Tsung-Hui
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York IEEE 2020 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:	Algorithms Array signal processing Beamforming Broadcasting antennas Communication networks Convergence Couplings Decomposition matrix factorization Multicast Multicast algorithms multicast beamforming Optimization Penalty dual decomposition Relays Signal processing algorithms Structured matrices sum-rate maximization
ISSN:	1053-587X, 1941-0476
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Abstract	In Part I of this paper, we proposed and analyzed a novel algorithmic framework, termed penalty dual decomposition (PDD), for the minimization of a nonconvex nonsmooth objective function, subject to difficult coupling constraints. Part II of this paper is devoted to evaluation of the proposed methods in the following three timely applications, ranging from communication networks to data analytics: i) the max-min rate fair multicast beamforming problem; ii) the sum-rate maximization problem in multi-antenna relay broadcast networks; and iii) the volume-min based structured matrix factorization problem. By exploiting the structure of the aforementioned problems, we show that effective algorithms for all these problems can be devised under the PDD framework. Unlike the state-of-the-art algorithms, the PDD-based algorithms are proven to achieve convergence to stationary solutions of the aforementioned nonconvex problems. Numerical results validate the efficacy of the proposed schemes.
AbstractList	In Part I of this paper, we proposed and analyzed a novel algorithmic framework, termed penalty dual decomposition (PDD), for the minimization of a nonconvex nonsmooth objective function, subject to difficult coupling constraints. Part II of this paper is devoted to evaluation of the proposed methods in the following three timely applications, ranging from communication networks to data analytics: i) the max-min rate fair multicast beamforming problem; ii) the sum-rate maximization problem in multi-antenna relay broadcast networks; and iii) the volume-min based structured matrix factorization problem. By exploiting the structure of the aforementioned problems, we show that effective algorithms for all these problems can be devised under the PDD framework. Unlike the state-of-the-art algorithms, the PDD-based algorithms are proven to achieve convergence to stationary solutions of the aforementioned nonconvex problems. Numerical results validate the efficacy of the proposed schemes.
Author	Chang, Tsung-Hui Hong, Mingyi Shi, Qingjiang Fu, Xiao
Author_xml	– sequence: 1 givenname: Qingjiang orcidid: 0000-0003-0507-9080 surname: Shi fullname: Shi, Qingjiang email: shiqj@tongji.edu.cn organization: School of Software Engineering, Tongji University, Shanghai, China – sequence: 2 givenname: Mingyi orcidid: 0000-0003-1263-9365 surname: Hong fullname: Hong, Mingyi email: mhong@umn.edu organization: Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN, USA – sequence: 3 givenname: Xiao orcidid: 0000-0003-4847-9586 surname: Fu fullname: Fu, Xiao email: xiao.fu@oregonstate.edu organization: School of EECS, Oregon State University, Corvallis, OR, USA – sequence: 4 givenname: Tsung-Hui orcidid: 0000-0003-1349-2764 surname: Chang fullname: Chang, Tsung-Hui email: changtsunghui@cuhk.edu.cn organization: Chinese University of Hong Kong, Shenzhen, China
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SubjectTerms	Algorithms Array signal processing Beamforming Broadcasting antennas Communication networks Convergence Couplings Decomposition matrix factorization Multicast Multicast algorithms multicast beamforming Optimization Penalty dual decomposition Relays Signal processing algorithms Structured matrices sum-rate maximization
Title	Penalty Dual Decomposition Method for Nonsmooth Nonconvex Optimization-Part II: Applications
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