2 citations · 3 across the 5 of their papers we have counts for
5 papers
A synthetic approach to comparison principles for variational problems, with applications to optimal transport
Flavien Léger, Maxime Sylvestre
We develop a synthetic, variational framework for deriving comparison principles in infinite-dimensional Banach spaces. Unlike traditional approaches that rely on the regularity of…
Nonnegative cross-curvature in infinite dimensions: synthetic definition and spaces of measures
Flavien Léger, Gabriele Todeschi, François-Xavier Vialard
Nonnegative cross-curvature (NNCC) is a geometric property of a cost function defined on a product space that originates in optimal transportation and the Ma-Trudinger-Wang theory.…
A geometric approach to apriori estimates for optimal transport maps
Simon Brendle, Flavien Léger, Robert J. McCann +1
A key inequality which underpins the regularity theory of optimal transport for costs satisfying the Ma--Trudinger--Wang condition is the Pogorelov second derivative bound. This tr…
Gradient descent with a general cost
Flavien Léger, Pierre-Cyril Aubin-Frankowski
We present a new class of gradient-type optimization methods that extends vanilla gradient descent, mirror descent, Riemannian gradient descent, and natural gradient descent. Our a…
A geometric Laplace method
Flavien Léger, François-Xavier Vialard
A classical tool for approximating integrals is the Laplace method. The first-order, as well as the higher-order Laplace formula is most often written in coordinates without any ge…