# Revisiting Projection-Free Optimization for Strongly Convex Constraint Sets

arXiv: https://arxiv.org/abs/1811.05831 · HTML: https://mlsanity.com/paper/1811.05831/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Nov 2018.

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

- [Local and Global Uniform Convexity Conditions](https://mlsanity.com/paper/2102.05134/) (2021)

## Abstract (arXiv)

We revisit the Frank-Wolfe (FW) optimization under strongly convex constraint sets. We provide a faster convergence rate for FW without line search, showing that a previously overlooked variant of FW is indeed faster than the standard variant. With line search, we show that FW can converge to the global optimum, even for smooth functions that are not convex, but are quasi-convex and locally-Lipschitz. We also show that, for the general case of (smooth) non-convex functions, FW with line search converges with high probability to a stationary point at a rate of Oleft(frac1tright), as long as the constraint set is strongly convex -- one of the fastest convergence rates in non-convex optimization.