Abstract
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.
Original language | English (US) |
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Article number | 9120361 |
Pages (from-to) | 4108-4122 |
Number of pages | 15 |
Journal | IEEE Transactions on Signal Processing |
Volume | 68 |
DOIs | |
State | Published - 2020 |
Externally published | Yes |
Bibliographical note
Publisher Copyright:© 1991-2012 IEEE.
Keywords
- BSUM
- KKT
- Penalty method
- augmented Lagrangian
- dual decomposition
- nonconvex optimization