Penalty dual decomposition method for nonsmooth nonconvex optimization - Part II: Applications

Qingjiang Shi, Mingyi Hong, Xiao Fu, Tsung Hui Chang

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


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.

Original languageEnglish (US)
Article number9119203
Pages (from-to)4242-4257
Number of pages16
JournalIEEE Transactions on Signal Processing
StatePublished - 2020
Externally publishedYes

Bibliographical note

Funding Information:
Manuscript received October 1, 2019; revised May 1, 2020; accepted June 4, 2020. Date of publication June 16, 2020; date of current version August 5, 2020. The associate editor coordinating the review of this article and approving it for publication was Prof. Nicolas Gillis. The work of Qingjiang Shi was supported in part by the National Key Research and Development Project under Grant 2017YFE0119300 and in part by the NSFC under Grants 61671411, 61731018, and U1709219. The work of Mingyi Hong was supported in part by the National Science Foundation under Grants CIF-1910385 and CNS-2003033 and in part by Army Research Office under Grant W911NF-19-1-0247. The work of Xiao Fu was supported in part by NSF ECCS under Grant 1608961 and in part by NSF ECCS under Grant 1808159, ARO W911NF-19-1-0247, ARO W911NF-19-1-0407. The work of Tsung-Hui Chang was supported in part by the National Key R&D Program of China under Grant 2018YFB1800800, in part by the NSFC, China, under Grant 61731018, and in part by the Shen-zhen Fundamental Research Fund under Grants JCYJ20190813171003723 and KQTD2015033114415450. Part of this article has been presented in IEEE ICASSP 2017. (Corresponding author: Mingyi Hong.) Qingjiang Shi is with the School of Software Engineering, Tongji University, Shanghai 201804, China, and also with the Shenzhen Research Institute of Big Data, Shenzhen 518172, China (e-mail:

Publisher Copyright:
© 1991-2012 IEEE.


  • Penalty dual decomposition
  • matrix factorization
  • multicast beamforming
  • sum-rate maximization


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