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Lecture
Optimal Transport: Brenier's Theorem
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Convex Optimization: Sets and Functions
Introduces convex optimization through sets and functions, covering intersections, examples, operations, gradient, Hessian, and real-world applications.
Convex Optimization: Elementary Results
Explores elementary results in convex optimization, including affine, convex, and conic hulls, proper cones, and convex functions.
Conjugate Duality: Understanding Convex Optimization
Explores conjugate duality in convex optimization, covering weak and supporting hyperplanes, subgradients, duality gap, and strong duality conditions.
Optimal Transport: Theory and Applications
Explores Lagrange multipliers, minimax theorems, and convex subsets in optimal transport theory.
Convex Optimization
Introduces convex optimization, focusing on the importance of convexity in algorithms and optimization problems.
Convexity: Functions and Global Minima
Explores convex functions, global minima, and their relationship with differentiability.
KKT and Convex Optimization
Covers the KKT conditions and convex optimization, discussing constraint qualifications and tangent cones of convex sets.
Convexity of Lovász Extension
Explores the convexity of Lovász extension and submodular function maximization, focusing on extending functions to convex sets and proving their convexity.