Metrics: Line and Convex Cone

Related lectures (28)

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

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

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

Explores Farkas' Lemma, hyperplane separation, combinatorics, and its application in game theory, focusing on penalty kick strategies.

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

Covers matrix kernels, images, linear applications, independence, and bases in vector spaces.

Explores linear dependence and independence of vectors in geometric spaces.

Explores systems of equations, vector operations, and geometric interpretations in linear algebra.

Explores linear combinations of vectors and matrices in Rn, demonstrating geometric interpretations and matrix operations.

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