Lectures related to Metrics: Line and Convex Cone

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.

Explores matrix operations, linear systems, solutions, and the span of vectors in linear algebra.

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

Explores linear independence in vector spaces and the concept of bases.

On Convex Optimization covers course organization, mathematical optimization problems, solution concepts, and optimization methods.

Explains linear independence, basis, and matrix rank with examples and exercises.

Covers the properties and operations of vector spaces, including addition and scalar multiplication.

Covers linear equations, vectors, and matrices, exploring their fundamental concepts and applications.

Introduces linear combinations of vectors in R^n and their properties.

Explores subspaces in linear algebra and transformations, including kernels and images of linear transformations.

Explores forming bases, dependencies, and relationships in linear applications using invertible matrices and canonical bases.