  The Frank-Wolfe algorithm is a method for constrained optimization that
relies on linear minimizations, as opposed to projections. Therefore, a
motivation put forward in a large body of work on the Frank-Wolfe algorithm is
the computational advantage of solving linear minimizations instead of
projections. However, the discussions supporting this advantage are often too
succinct or incomplete. In this paper, we review the complexity bounds for both
tasks on several sets commonly used in optimization. Projection methods onto
the $\ell_p$-ball, $p\in\left]1,2\right[\cup\left]2,+\infty\right[$, and the
Birkhoff polytope are also proposed.

Optimization and Control;Data Structures and Algorithms;Machine Learning