Optimal Transport: Convexity and Inequalities

Related lectures (29)

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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.

Covers the description of all solutions of the initial problem and related concepts such as compactness and closure.

Explores elementary results in convex optimization, including affine, convex, and conic hulls, proper cones, and convex functions.