mlsanityData to 7 Oct 2026

Heavy Ball Momentum for Conditional Gradient

arXiv 2110.04243 ↗First posted 8 Oct 2021math.OC cs.LGcited by 7

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Abstract (arXiv)

Conditional gradient, aka Frank Wolfe (FW) algorithms, have well-documented merits in machine learning and signal processing applications. Unlike projection-based methods, momentum cannot improve the convergence rate of FW, in general. This limitation motivates the present work, which deals with heavy ball momentum, and its impact to FW. Specifically, it is established that heavy ball offers a unifying perspective on the primal-dual (PD) convergence, and enjoys a tighter per iteration PD error rate, for multiple choices of step sizes, where PD error can serve as the stopping criterion in practice. In addition, it is asserted that restart, a scheme typically employed jointly with Nesterov's momentum, can further tighten this PD error bound. Numerical results demonstrate the usefulness of heavy ball momentum in FW iterations.

Key facts. Cited by 7 papers in the map (data through 7 Oct 2026). Builds on 16 of its 39 references that are in the map. First posted on arXiv 8 Oct 2021.

Builds on

16 of 39 references.

References · 16

  1. 2015On the Global Linear Convergence of Frank-Wolfe Optimization Variantscited by 76
  2. 2020Good Subnetworks Provably Exist: Pruning via Greedy Forward Selectioncited by 70
  3. 2014Global convergence of the Heavy-ball method for convex optimizationcited by 60
  4. 2018Stochastic Conditional Gradient Methods: From Convex Minimization to Submodular Maximizationcited by 47
  5. 2014Faster Rates for the Frank-Wolfe Method over Strongly-Convex Setscited by 42
  6. 2019One Sample Stochastic Frank-Wolfecited by 32
  7. 2013The Complexity of Large-scale Convex Programming under a Linear Optimization Oraclecited by 27
  8. 2017The Approximate Duality Gap Technique: A Unified Theory of First-Order Methodscited by 27
  9. 2019Sinkhorn Barycenters with Free Support via Frank-Wolfe Algorithmcited by 27
  10. 2015Sequential Kernel Herding: Frank-Wolfe Optimization for Particle Filteringcited by 22
  11. 2013New Analysis and Results for the Frank-Wolfe Methodcited by 17
  12. 2015An Extended Frank-Wolfe Method with "In-Face" Directions, and its Application to Low-Rank Matrix Completioncited by 15
4 more
  1. 2017Linear Convergence of a Frank-Wolfe Type Algorithm over Trace-Norm Ballscited by 15
  2. 2013Conditional Gradient Algorithms for Norm-Regularized Smooth Convex Optimizationcited by 13
  3. 2021Memory-Efficient Convex Optimization for Self-Dictionary Separable Nonnegative Matrix Factorization: A Frank-Wolfe Approachcited by 6
  4. 2016Randomized Block Frank-Wolfe for Convergent Large-Scale Learningcited by 1

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 3; 2024: 0; 2025: 3; 2026: 1.

7 papers.

  1. 2025Lions and Muons: Optimization via Stochastic Frank-Wolfe under Heavy-Tailed Noisecited by 38
  2. 2023Enhancing Sharpness-Aware Optimization Through Variance Suppressioncited by 37
  3. 2023Scaling Up Differentially Private LASSO Regularized Logistic Regression via Faster Frank-Wolfe Iterationscited by 8
  4. 2025Provable Benefit of SignGD: A Minimal Model Under Heavy-Tailed Class Imbalancecited by 3
  5. 2025VASSO: Variance Suppression for Sharpness-Aware Minimizationcited by 1
  6. 2026Adaptive Lipschitz-Free Conditional Gradient Methods for Stochastic Composite Nonconvex Optimizationcited by 1
  7. 2023Conic Descent Redux for Memory-Efficient Optimizationcited by 0