Optimal Transport: Convexity and Inequalities

Related lectures (36)

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.

Introduces convex sets and functions, discussing minimizers, optimality conditions, and characterizations, along with examples and key inequalities.

Explores the approximation of the zeta function using compact functions and spectral decomposition.

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

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

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

Covers the preliminaries in measure theory, including loc comp, separable, complete metric space, and tightness concepts.

Explores convex sets, Minkowski-Weyl theorem, and Separation theorem in convex analysis.

Covers the concept of convex functions and their applications in optimization problems.

Covers the proof of the Jordan Curve Theorem and the properties of embedded spheres.

Explores harmonic forms on Riemann surfaces, covering uniqueness of solutions and the Riemann bilinear identity.

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.

Explores the proof of Weyl's theorem, focusing on discrete spectrum, ground states, and potential energy continuity.

Explores convex functions, global minima, and their relationship with differentiability.

Covers the concept of compact embedding in Banach spaces and Sobolev inequalities.

Explores optimal transport regularity and Brenier's theorem, discussing continuity and convexity concepts.

Covers the Cantor-Heine theorem, discussing uniform continuity and compactness.

Covers the Hadamard factorisation theorem for entire functions of order at most 1.

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