English

Secant Line Search for Frank-Wolfe Algorithms

Optimization and Control 2025-06-11 v2

Abstract

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.

Keywords

Cite

@article{arxiv.2501.18775,
  title  = {Secant Line Search for Frank-Wolfe Algorithms},
  author = {Deborah Hendrych and Mathieu Besançon and David Martínez-Rubio and Sebastian Pokutta},
  journal= {arXiv preprint arXiv:2501.18775},
  year   = {2025}
}
R2 v1 2026-06-28T21:26:41.693Z