mlsanityData to 7 Oct 2026

Splitting methods with variable metric for KL functions

arXiv 1405.1357 ↗First posted 6 May 2014math.OCcited by 26

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Abstract (arXiv)

We study the convergence of general abstract descent methods applied to a lower semicontinuous nonconvex function f that satisfies the Kurdyka-Lojasiewicz inequality in a Hilbert space. We prove that any precompact sequence converges to a critical point of f and obtain new convergence rates both for the values and the iterates. The analysis covers alternating versions of the forward-backward method with variable metric and relative errors. As an example, a nonsmooth and nonconvex version of the Levenberg-Marquardt algorithm is detailled.

Key facts. Cited by 26 papers in the map (data through 7 Oct 2026). First posted on arXiv 6 May 2014.

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Citing papers per year: 2021: 4; 2022: 6; 2023: 5; 2024: 3; 2025: 2; 2026: 6.

26 papers.

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  1. 2023What's in a Prior? Learned Proximal Networks for Inverse Problemscited by 24
  2. 2021Proximal Gradient Descent-Ascent: Variable Convergence under KL Geometrycited by 17
  3. 2021Convergence of Random Reshuffling Under The Kurdyka-Lojasiewicz Inequalitycited by 16
  4. 2021A Scalable Second Order Method for Ill-Conditioned Matrix Completion from Few Samplescited by 13
  5. 2022Nonsmooth Nonconvex-Nonconcave Minimax Optimization: Primal-Dual Balancing and Iteration Complexity Analysiscited by 12
  6. 2022Cyclic Block Coordinate Descent With Variance Reduction for Composite Nonconvex Optimizationcited by 9
  7. 2022A Fast and Convergent Proximal Algorithm for Regularized Nonconvex and Nonsmooth Bi-level Optimizationcited by 7
  8. 2023Convergence Analysis of Mean Shiftcited by 6
  9. 2024Learning pseudo-contractive denoisers for inverse problemscited by 6
  10. 2022Gradient descent provably escapes saddle points in the training of shallow ReLU networkscited by 5
  11. 2023A Normal Map-Based Proximal Stochastic Gradient Method: Convergence and Identification Propertiescited by 5
  12. 2022Hybrid ISTA: Unfolding ISTA With Convergence Guarantees Using Free-Form Deep Neural Networkscited by 4
14 more
  1. 2022Convergence Rates of Training Deep Neural Networks via Alternating Minimization Methodscited by 4
  2. 2023A New Random Reshuffling Method for Nonsmooth Nonconvex Finite-sum Optimizationcited by 4
  3. 2025Learning Cocoercive Conservative Denoisers via Helmholtz Decomposition for Poisson Inverse Problemscited by 4
  4. 2023Restarts subject to approximate sharpness: A parameter-free and optimal scheme for first-order methodscited by 2
  5. 2021WARPd: A linearly convergent first-order method for inverse problems with approximate sharpness conditionscited by 1
  6. 2024Convergence Analysis of Blurring Mean Shiftcited by 1
  7. 2025A first-order method for nonconvex-nonconcave minimax problems under a local Kurdyka-Lojasiewicz conditioncited by 1
  8. 2024Stochastic Gradient Descent Revisitedcited by 0
  9. 2026A block-coordinate descent framework for non-convex composite optimization. Application to sparse precision matrix estimationcited by 0
  10. 2026Dynamic Proximal Gradient Algorithms for Schatten-p Quasi-Norm Regularized Problemscited by 0
  11. 2026Memory-Computation Tradeoffs in Semi Amortized Parametric Optimizationcited by 0
  12. 2026A proximal subgradient method for nonconvex stochastic optimization under the Kurdyka-Lojasiewicz conditioncited by 0
  13. 2026Information Bottleneck under Perfect Privacycited by 0
  14. 2026GCA: Global Centroid Alignment in Federated Learningcited by 0