mlsanityData to 7 Oct 2026

Gradient Sampling Methods for Nonsmooth Optimization

arXiv 1804.11003 ↗First posted 29 Apr 2018math.OCcited by 23

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Abstract (arXiv)

This paper reviews the gradient sampling methodology for solving nonsmooth, nonconvex optimization problems. An intuitively straightforward gradient sampling algorithm is stated and its convergence properties are summarized. Throughout this discussion, we emphasize the simplicity of gradient sampling as an extension of the steepest descent method for minimizing smooth objectives. We then provide overviews of various enhancements that have been proposed to improve practical performance, as well as of several extensions that have been made in the literature, such as to solve constrained problems. The paper also includes clarification of certain technical aspects of the analysis of gradient sampling algorithms, most notably related to the assumptions one needs to make about the set of points at which the objective is continuously differentiable. Finally, we discuss possible future research directions.

Key facts. Cited by 23 papers in the map (data through 7 Oct 2026). First posted on arXiv 29 Apr 2018.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 4; 2022: 4; 2023: 5; 2024: 6; 2025: 1; 2026: 3.

23 papers.

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  1. 2022Gradient-Free Methods for Deterministic and Stochastic Nonsmooth Nonconvex Optimizationcited by 40
  2. 2024Diffusion Models as Constrained Samplers for Optimization with Unknown Constraintscited by 33
  3. 2023Deterministic Nonsmooth Nonconvex Optimizationcited by 25
  4. 2023Efficient Gradient Approximation Method for Constrained Bilevel Optimizationcited by 15
  5. 2021Training Recurrent Neural Networks by Sequential Least Squares and the Alternating Direction Method of Multiplierscited by 8
  6. 2024An L-BFGS-B approach for linear and nonlinear system identification under ℓ1 and group-Lasso regularizationcited by 8
  7. 2022Towards a Theoretical Foundation of Policy Optimization for Learning Control Policiescited by 6
  8. 2022Global Convergence of Direct Policy Search for State-Feedback H_∞ Robust Control: A Revisit of Nonsmooth Synthesis with Goldstein Subdifferentialcited by 6
  9. 2023Optimization and Optimizers for Adversarial Robustnesscited by 6
  10. 2023Smoothing Methods for Automatic Differentiation Across Conditional Branchescited by 6
  11. 2021Model-Free μ Synthesis via Adversarial Reinforcement Learningcited by 5
  12. 2024D-GRIL: End-to-End Topological Learning with 2-parameter Persistencecited by 5
11 more
  1. 2021Survey Descent: A Multipoint Generalization of Gradient Descent for Nonsmooth Optimizationcited by 4
  2. 2022Optimization for Robustness Evaluation beyond ℓp Metricscited by 3
  3. 2023Stochastic Gradient Sampling for Enhancing Neural Networks Trainingcited by 3
  4. 2024Finite Neural Networks as Mixtures of Gaussian Processes: From Provable Error Bounds to Prior Selectioncited by 3
  5. 2026The Normalized Maximum Likelihood for Regular Non-Smooth Models: Measure-Theoretic Foundations and Geometric Samplingcited by 1
  6. 2021Markov subsampling based Huber Criterioncited by 0
  7. 2024Model-Free μ-Synthesis: A Nonsmooth Optimization Perspectivecited by 0
  8. 2024SPGD: Steepest Perturbed Gradient Descent Optimizationcited by 0
  9. 2025Permutation Randomization on Nonsmooth Nonconvex Optimization: A Theoretical and Experimental Studycited by 0
  10. 2026Lipschitzian SLLNs for random functionscited by 0
  11. 2026The Exponential Price of Determinism in Nonsmooth Nonconvex Optimizationcited by 0