mlsanityData to 7 Oct 2026

Inertial Proximal Alternating Linearized Minimization (iPALM) for Nonconvex and Nonsmooth Problems

arXiv 1702.02505 ↗First posted 8 Feb 2017math.OCcited by 40

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Abstract (arXiv)

In this paper we study nonconvex and nonsmooth optimization problems with semi-algebraic data, where the variables vector is split into several blocks of variables. The problem consists of one smooth function of the entire variables vector and the sum of nonsmooth functions for each block separately. We analyze an inertial version of the Proximal Alternating Linearized Minimization (PALM) algorithm and prove its global convergence to a critical point of the objective function at hand. We illustrate our theoretical findings by presenting numerical experiments on blind image deconvolution, on sparse non-negative matrix factorization and on dictionary learning, which demonstrate the viability and effectiveness of the proposed method.

Key facts. Cited by 40 papers in the map (data through 7 Oct 2026). First posted on arXiv 8 Feb 2017.

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Citing papers per year: 2021: 9; 2022: 6; 2023: 6; 2024: 9; 2025: 7; 2026: 3.

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  2. 2022Stable Deep MRI Reconstruction using Generative Priorscited by 21
  3. 2021Convergence of Random Reshuffling Under The Kurdyka-Lojasiewicz Inequalitycited by 16
  4. 2023Explicit Diffusion of Gaussian Mixture Model Based Image Priorscited by 6
  5. 2023Learned Alternating Minimization Algorithm for Dual-domain Sparse-View CT Reconstructioncited by 6
  6. 2022Proximal Residual Flows for Bayesian Inverse Problemscited by 5
  7. 2021Block Alternating Bregman Majorization Minimization with Extrapolationcited by 4
  8. 2022Deep, Deep Learning with BARTcited by 4
  9. 2024A Momentum Accelerated Algorithm for ReLU-based Nonlinear Matrix Decompositioncited by 4
  10. 2025An Accelerated Alternating Partial Bregman Algorithm for ReLU-based Matrix Decompositioncited by 4
  11. 2021Inertial Proximal Deep Learning Alternating Minimization for Efficient Neutral Network Trainingcited by 3
  12. 2021A Framework of Inertial Alternating Direction Method of Multipliers for Non-Convex Non-Smooth Optimizationcited by 3
28 more
  1. 2023Efficiently Factorizing Boolean Matrices using Proximal Gradient Descentcited by 3
  2. 2023An Accelerated Block Proximal Framework with Adaptive Momentum for Nonconvex and Nonsmooth Optimizationcited by 3
  3. 2024Learning of Patch-Based Smooth-Plus-Sparse Models for Image Reconstructioncited by 3
  4. 2025Plug-and-Play Image Restoration with Flow Matching: A Continuous Viewpointcited by 3
  5. 2021Structured Sparse Non-negative Matrix Factorization with L20-Norm for scRNA-seq Data Analysiscited by 2
  6. 2023Joint Non-Linear MRI Inversion with Diffusion Priorscited by 2
  7. 2024Graph Regularized NMF with L20-norm for Unsupervised Feature Learningcited by 2
  8. 2021Spatially Coherent Clustering Based on Orthogonal Nonnegative Matrix Factorizationcited by 1
  9. 2024Block Majorization Minimization with Extrapolation and Application to β-NMFcited by 1
  10. 2025Adaptive Lipschitz-Free Proximal Gradient Methods for Stochastic Composite Nonconvex Optimizationcited by 1
  11. 2025A Triple-Inertial Accelerated Alternating Optimization Method for Deep Learning Trainingcited by 1
  12. 2025An Efficient Alternating Algorithm for ReLU-based Symmetric Matrix Decompositioncited by 1
  13. 2026MotionDPS: Motion-Compensated 3D Brain MRI Reconstructioncited by 1
  14. 2021Time series forecasting from partial observations via Non-negative Matrix Factorizationcited by 0
  15. 2021A Refined Inertial DC Algorithm for DC Programmingcited by 0
  16. 2021On-the-Fly Rectification for Robust Large-Vocabulary Topic Inferencecited by 0
  17. 2022Unsupervised energy disaggregation via convolutional sparse codingcited by 0
  18. 2022A Variational Approach for Joint Image Recovery and Feature Extraction Based on Spatially-Varying Generalised Gaussian Modelscited by 0
  19. 2023Globally Convergent Accelerated Algorithms for Multilinear Sparse Logistic Regression with ℓ0-constraintscited by 0
  20. 2024Edge-guided Low-light Image Enhancement with Inertial Bregman Alternating Linearized Minimizationcited by 0
  21. 2024Convergence of the majorized PAM method with subspace correction for low-rank composite factorization modelcited by 0
  22. 2024Federated Binary Matrix Factorization using Proximal Optimizationcited by 0
  23. 2024LAMA: Stable Dual-Domain Deep Reconstruction For Sparse-View CTcited by 0
  24. 2024A Learned Proximal Alternating Minimization Algorithm and Its Induced Network for a Class of Two-block Nonconvex and Nonsmooth Optimizationcited by 0
  25. 2025LAMA-Net: A Convergent Network Architecture for Dual-Domain Reconstructioncited by 0
  26. 2025DualHash: A Stochastic Primal-Dual Algorithm with Theoretical Guarantee for Deep Hashingcited by 0
  27. 2026An Inertial Block Proximal Linearized Method with Adaptive Momentum for Nonconvex and Nonsmooth Optimizationcited by 0
  28. 2026Generalized Geometry Block Proximal Linearized Method for Multiblock Nonconvex and Nonsmooth Optimizationcited by 0