# Secant Line Search for Frank-Wolfe Algorithms

arXiv: https://arxiv.org/abs/2501.18775 · HTML: https://mlsanity.com/paper/2501.18775/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jan 2025.

## Built on by (most cited first, 2 of 2)

- [Scalable DC Optimization via Adaptive Frank-Wolfe Algorithms](https://mlsanity.com/paper/2507.17545/) (2025)
- [Adaptive Conditional Gradient Descent](https://mlsanity.com/paper/2510.11440/) (2025)

## Abstract (arXiv)

We present a new step-size strategy based on the secant method for Frank-Wolfe algorithms. This strategy, which requires mild assumptions about the function under consideration, can be applied to any Frank-Wolfe algorithm. It is as effective as full line search and, in particular, allows for adapting to the local smoothness of the function, such as in Pedregosa et al 2018, but comes with a significantly reduced computational cost, leading to higher effective rates of convergence. We provide theoretical guarantees and demonstrate the effectiveness of the strategy through numerical experiments.