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

• Published in: IEEE transactions on signal processing Vol. 68; pp. 4242 - 4257
• Main Authors: Shi, Qingjiang, Hong, Mingyi, Fu, Xiao, Chang, Tsung-Hui
• Format: Journal Article
• Language: English
• Published: New York IEEE 2020; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: 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
• DOI: 10.1109/TSP.2020.3001397

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.