Convex Optimization: Convex Functions

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

Covers the properties and operations of convex functions.

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

Explores convex sets, their properties, and applications in optimization.

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

Covers essential linear algebra concepts for convex optimization, including vector norms, eigenvalue decomposition, and matrix properties.

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

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

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

Explores optimization on convex sets, including KKT points and tangent cones.