期刊
IEEE TRANSACTIONS ON SIGNAL PROCESSING
卷 68, 期 -, 页码 4108-4122出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TSP.2020.3001906
关键词
Signal processing algorithms; Optimization; Couplings; Relays; Convergence; Minimization; Signal processing; Penalty method; dual decomposition; BSUM; KKT; augmented Lagrangian; nonconvex optimization
资金
- National Key Research and Development Project [2017YFE0119300]
- NSFC [61671411, 61731018, U1709219]
- National Science Foundation [CIF-1910385, CMMI-172775]
- Army Research Office [W911NF-19-1-0247]
Many contemporary signal processing, machine learning and wireless communication applications can be formulated as nonconvex nonsmooth optimization problems. Often there is a lack of efficient algorithms for these problems, especially when the optimization variables are nonlinearly coupled in some nonconvex constraints. In this work, we propose an algorithm named penalty dual decomposition (PDD) for these difficult problems and discuss its various applications. The PDD is a double-loop iterative algorithm. Its inner iteration is used to inexactly solve a nonconvex nonsmooth augmented Lagrangian problem via block-coordinate-descent-type methods, while its outer iteration updates the dual variables and/or a penalty parameter. In Part I of this work, we describe the PDD algorithm and establish its convergence to KKT solutions. In Part II we evaluate the performance of PDD by customizing it to three applications arising from signal processing and wireless communications.
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