# Conditional Gradient Methods

arXiv: https://arxiv.org/abs/2211.14103 · HTML: https://mlsanity.com/paper/2211.14103/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Nov 2022.

## Built on by (most cited first, 17 of 17)

- [Lions and Muons: Optimization via Stochastic Frank-Wolfe under Heavy-Tailed Noise](https://mlsanity.com/paper/2506.04192/) (2025)
- [Sarah Frank-Wolfe: Methods for Constrained Optimization with Best Rates and Practical Features](https://mlsanity.com/paper/2304.11737/) (2023)
- [Unified Projection-Free Algorithms for Adversarial DR-Submodular Optimization](https://mlsanity.com/paper/2403.10063/) (2024)
- [Linearization Algorithms for Fully Composite Optimization](https://mlsanity.com/paper/2302.12808/) (2023)
- [DFWLayer: Differentiable Frank-Wolfe Optimization Layer](https://mlsanity.com/paper/2308.10806/) (2023)
- [Don't Be Greedy, Just Relax! Pruning LLMs via Frank-Wolfe](https://mlsanity.com/paper/2510.13713/) (2025)
- [Principled and Scalable Diversity-Aware Retrieval via Cardinality-Constrained Binary Quadratic Programming](https://mlsanity.com/paper/2604.02554/) (2026)
- [ScoreFusion: Fusing Score-based Generative Models via Kullback-Leibler Barycenters](https://mlsanity.com/paper/2406.19619/) (2024)
- [MaskPro: Linear-Space Probabilistic Learning for Strict (N:M)-Sparsity on LLMs](https://mlsanity.com/paper/2506.12876/) (2025)
- [First-Order Sparse Convex Optimization: Better Rates with Sparse Updates](https://mlsanity.com/paper/2506.19075/) (2025)
- [Scalable DC Optimization via Adaptive Frank-Wolfe Algorithms](https://mlsanity.com/paper/2507.17545/) (2025)
- [Adaptive Lipschitz-Free Conditional Gradient Methods for Stochastic Composite Nonconvex Optimization](https://mlsanity.com/paper/2603.06369/) (2026)
- [CellBRIDGE: Learning Cellular Trajectories via Interaction-Aware Alignment](https://mlsanity.com/paper/2605.30635/) (2026)
- [Faster Accelerated First-order Methods for Convex Optimization with Strongly Convex Function Constraints](https://mlsanity.com/paper/2212.11143/) (2022)
- [Linear Convergence of the Frank-Wolfe Algorithm over Product Polytopes](https://mlsanity.com/paper/2505.11259/) (2025)
- [Broximal Gradient Descent: A Projection-Free Sister of Projected Gradient Descent](https://mlsanity.com/paper/2605.08850/) (2026)
- [Zero-order Parameter-free Optimization for LMO-based Methods: Novel Approach for Efficient Fine-tuning](https://mlsanity.com/paper/2606.14970/) (2026)

## Abstract (arXiv)

The purpose of this survey is to serve both as a gentle introduction and a coherent overview of state-of-the-art Frank--Wolfe algorithms, also called conditional gradient algorithms, for function minimization. These algorithms are especially useful in convex optimization when linear optimization is cheaper than projections. The selection of the material has been guided by the principle of highlighting crucial ideas as well as presenting new approaches that we believe might become important in the future, with ample citations even of old works imperative in the development of newer methods. Yet, our selection is sometimes biased, and need not reflect consensus of the research community, and we have certainly missed recent important contributions. After all the research area of Frank--Wolfe is very active, making it a moving target. We apologize sincerely in advance for any such distortions and we fully acknowledge: We stand on the shoulder of giants.