Optimal Transport: Regularity and Brenier's Theorem

Related lectures (28)

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Explores geodesic convexity in metric spaces and its applications, discussing properties and the stability of inequalities.

Explores the Rockafellar Theorem in optimal transport, focusing on c-cyclical monotonicity and convex functions.

Explores VC dimension, gradient descent, convex sets, and Lipschitz functions in convex optimization.

Covers distributions, derivatives, convergence, and continuity criteria in function spaces.

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Explores optimal transport, emphasizing convexity properties and inequalities in compact sets.

Covers the KKT conditions and convex optimization, discussing constraint qualifications and tangent cones of convex sets.

Explores Lagrange multipliers, minimax theorems, and convex subsets in optimal transport theory.

Discusses approximation by smooth functions and the convergence of function sequences in normed vector spaces.