# Efficient Quadratic Corrections for Frank-Wolfe Algorithms

arXiv: https://arxiv.org/abs/2506.02635 · HTML: https://mlsanity.com/paper/2506.02635/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jun 2025.

## Built on by (most cited first, 1 of 1)

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

## Abstract (arXiv)

We develop a Frank-Wolfe algorithm with corrective steps, generalizing previous algorithms including blended conditional gradients, blended pairwise conditional gradients, and fully-corrective Frank-Wolfe. For this, we prove tight convergence guarantees together with an optimal face identification property. Furthermore, we propose two highly efficient corrective steps for convex quadratic objectives based on linear optimization or linear system solving, akin to Wolfe's minimum-norm point, and show that they converge in finite time under suitable conditions. Beyond optimization problems that are directly quadratic, we revisit two algorithms - split conditional gradient and second-order conditional gradient sliding - which can leverage quadratic corrections to accelerate their quadratic subproblems. We demonstrate improved convergence rates for the first and broader applicability for the second, which may be of independent interest. Finally, we show substantial computational speedups for Frank-Wolfe-based algorithms with quadratic corrections across the considered problem classes.