Accelerating conditional gradient methods.

Summary The Frank-Wolfe algorithms, a.k.a. conditional gradient algorithms, solve constrained optimization problems. They break down a non-linear problem into a series of linear minimization on the constraint set. This contributes to their recent revival in many applied domains, in particular those involving large-scale optimization problems. In this dissertation, we design or analyze versions of the Frank-Wolfe algorithms. We notably show that, contrary to other types of algorithms, this family is adaptive to a broad spectrum of structural assumptions, without the need to know and specify the parameters controlling these hypotheses.