Penalty Dual Decomposition Method For Nonsmooth Nonconvex Optimization

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 iterations is used to inexactly solve a nonconvex nonsmooth augmented Lagrangian problem via block-coordinate-descenttype 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 rigorously 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.

Two part paper, 27 figures

References in corpus (10)

• A Variable Splitting Augmented Lagrangian Approach to Linear Spectral Unmixing
• Projection onto the probability simplex: An efficient algorithm with a simple proof, and an application
• Joint Source and Relay Precoding Designs for MIMO Two-Way Relaying Based on MSE Criterion
• A General Robust Linear Transceiver Design for Multi-Hop Amplify-and-Forward MIMO Relaying Systems
• Identifiability of the Simplex Volume Minimization Criterion for Blind Hyperspectral Unmixing: The No Pure-Pixel Case
• Robust Volume Minimization-Based Matrix Factorization for Remote Sensing and Document Clustering
• Cooperative Algorithms for MIMO Amplify-and-Forward Relay Networks
• Joint Source-Relay Design for Full--Duplex MIMO AF Relay Systems
• Joint Filter and Waveform Design for Radar STAP in Signal Dependent Interference
• Cross-layer design for downlink multi-hop cloud radio access networks with network coding

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