# Frank-Wolfe and friends: a journey into projection-free first-order optimization methods

arXiv: https://arxiv.org/abs/2106.10261 · HTML: https://mlsanity.com/paper/2106.10261/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Jun 2021.

## Built on by (most cited first, 10 of 10)

- [Exploiting the Curvature of Feasible Sets for Faster Projection-Free Online Learning](https://mlsanity.com/paper/2205.11470/) (2022)
- [Q-FW: A Hybrid Classical-Quantum Frank-Wolfe for Quadratic Binary Optimization](https://mlsanity.com/paper/2203.12633/) (2022)
- [Scaling Up Differentially Private LASSO Regularized Logistic Regression via Faster Frank-Wolfe Iterations](https://mlsanity.com/paper/2310.19978/) (2023)
- [Adaptive Conditional Gradient Descent](https://mlsanity.com/paper/2510.11440/) (2025)
- [Convex optimization over a probability simplex](https://mlsanity.com/paper/2305.09046/) (2023)
- [Learning the Right Layers: a Data-Driven Layer-Aggregation Strategy for Semi-Supervised Learning on Multilayer Graphs](https://mlsanity.com/paper/2306.00152/) (2023)
- [Federated Frank-Wolfe Algorithm](https://mlsanity.com/paper/2408.10090/) (2024)
- [Quantum Algorithms for Projection-Free Sparse Convex Optimization](https://mlsanity.com/paper/2507.08543/) (2025)
- [Empirical evaluation of the Frank-Wolfe methods for constructing white-box adversarial attacks](https://mlsanity.com/paper/2512.10936/) (2025)
- [Zero-order Parameter-free Optimization for LMO-based Methods: Novel Approach for Efficient Fine-tuning](https://mlsanity.com/paper/2606.14970/) (2026)

## Abstract (arXiv)

Invented some 65 years ago in a seminal paper by Marguerite Straus-Frank and Philip Wolfe, the Frank-Wolfe method recently enjoys a remarkable revival, fuelled by the need of fast and reliable first-order optimization methods in Data Science and other relevant application areas. This review tries to explain the success of this approach by illustrating versatility and applicability in a wide range of contexts, combined with an account on recent progress in variants, both improving on the speed and efficiency of this surprisingly simple principle of first-order optimization.