mlsanityData to 14 Oct 2026

Adaptive Proximal Gradient Method for Convex Optimization

arXiv 2308.02261 ↗First posted 4 Aug 2023math.OC cs.LG cs.NAcited by 21

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Abstract (arXiv)

In this paper, we explore two fundamental first-order algorithms in convex optimization, namely, gradient descent (GD) and proximal gradient method (ProxGD). Our focus is on making these algorithms entirely adaptive by leveraging local curvature information of smooth functions. We propose adaptive versions of GD and ProxGD that are based on observed gradient differences and, thus, have no added computational costs. Moreover, we prove convergence of our methods assuming only local Lipschitzness of the gradient. In addition, the proposed versions allow for even larger stepsizes than those initially suggested in [MM20].

Key facts. Cited by 21 papers in the map (data through 14 Oct 2026). Builds on 11 of its 19 references that are in the map. First posted on arXiv 4 Aug 2023.

Builds on

11 of 19 references.

References · 11

  1. 2021Convex optimizationcited by 2,515
  2. 2023Learning-Rate-Free Learning by D-Adaptationcited by 113
  3. 2023DoG is SGD's Best Friend: A Parameter-Free Dynamic Step Size Schedulecited by 85
  4. 2019Adaptive Gradient Descent without Descentcited by 79
  5. 2018Golden Ratio Algorithms for Variational Inequalitiescited by 38
  6. 2023DoWG Unleashed: An Efficient Universal Parameter-Free Gradient Descent Methodcited by 35
  7. 2023Provably Faster Gradient Descent via Long Stepscited by 20
  8. 2023Adaptive proximal algorithms for convex optimization under local Lipschitz continuity of the gradientcited by 19
  9. 2021A first-order primal-dual method with adaptivity to local smoothnesscited by 7
  10. 2016The variable metric forward-backward splitting algorithm under mild differentiability assumptionscited by 3
  11. 2015On the convergence of the forward-backward splitting method with linesearchescited by 1

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 2; 2024: 4; 2025: 10; 2026: 5.

21 papers.

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  1. 2023A simple uniformly optimal method without line search for convex optimizationcited by 18
  2. 2024Adaptive proximal gradient methods are universal without approximationcited by 4
  3. 2024Stochastic Weakly Convex Optimization Beyond Lipschitz Continuitycited by 3
  4. 2025Gradient Methods with Online Scaling Part I. Theoretical Foundationscited by 3
  5. 2023On the convergence of adaptive first order methods: proximal gradient and alternating minimization algorithmscited by 2
  6. 2025Sparse Polyak: an adaptive step size rule for high-dimensional M-estimationcited by 2
  7. 2025First-ish Order Methods: Hessian-aware Scalings of Gradient Descentcited by 1
  8. 2025Online Learning-guided Learning Rate Adaptation via Gradient Alignmentcited by 1
  9. 2025Adaptive Conditional Gradient Descentcited by 1
  10. 2026Randomized Feasibility Methods for Constrained Optimization with Adaptive Step Sizescited by 1
  11. 2024Safeguarding adaptive methods: global convergence of Barzilai-Borwein and other stepsize choicescited by 0
  12. 2024Quantum Algorithm for Sparse Online Learning with Truncated Gradient Descentcited by 0
9 more
  1. 2025Robust Spatiotemporal Epidemic Modeling with Integrated Adaptive Outlier Detectioncited by 0
  2. 2025Stochastic Adaptive Gradient Descent Without Descentcited by 0
  3. 2025AutoGD: Automatic Learning Rate Selection for Gradient Descentcited by 0
  4. 2025Robust Non-negative Proximal Gradient Algorithm for Inverse Problemscited by 0
  5. 2025Sparse Polyak with optimal thresholding operators for high-dimensional M-estimationcited by 0
  6. 2026Adaptive Decentralized Composite Optimization via Three-Operator Splittingcited by 0
  7. 2026Adaptive Delayed-Update Cyclic Algorithm for Variational Inequalitiescited by 0
  8. 2026Stochastic Auto-conditioned Fast Gradient Methods with Optimal Ratescited by 0
  9. 2026Adaptive Bregman Proximal Stochastic Gradient with a Stabilized Barzilai--Borwein Step Sizecited by 0