# Affine invariant convergence rates of the conditional gradient method

arXiv: https://arxiv.org/abs/2112.06727 · HTML: https://mlsanity.com/paper/2112.06727/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Dec 2021.

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

- [Gauges and Accelerated Optimization over Smooth and/or Strongly Convex Sets](https://mlsanity.com/paper/2303.05037/) (2023)
- [Linear Convergence of the Frank-Wolfe Algorithm over Product Polytopes](https://mlsanity.com/paper/2505.11259/) (2025)

## Abstract (arXiv)

We show that the conditional gradient method for the convex composite problem [minxf(x) + Psi(x)] generates primal and dual iterates with a duality gap converging to zero provided a suitable em growth property holds and the algorithm makes a judicious choice of stepsizes. The rate of convergence of the duality gap to zero ranges from sublinear to linear depending on the degree of the growth property. The growth property and convergence results depend on the pair (f,Psi) in an affine invariant and norm-independent fashion.