Lectures related to Absolutely convex set

Convex Optimization: Convex Functions

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

Optimal Transport: Rockafellar Theorem

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

Cones of convex sets

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

Convex Optimization: Gradient Descent

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

Convex Sets: Theory and Applications

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

KKT and Convex Optimization

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

Convex Functions

Covers the properties and operations of convex functions.

Diophantine Approximation: Minbowski's Theorem

Covers Minbowski's Theorem on Diophantine Approximation and Gram-Schmidt orthogonalization.

Separation Theorem: Convex Sets

Explores the Second Separation Theorem for closed convex sets and the concept of supporting hyperplanes.

Geodesic Convexity: Basic Definitions

Introduces geodesic convexity on Riemannian manifolds and explores its properties.

Optimal Transport: Theory and Applications

Explores Lagrange multipliers, minimax theorems, and convex subsets in optimal transport theory.

Convex Optimization: Elementary Results

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

Optimization Techniques: Convexity and Algorithms in Machine Learning

Covers optimization techniques in machine learning, focusing on convexity, algorithms, and their applications in ensuring efficient convergence to global minima.

Convex Optimization: Sets and Functions

Introduces convex optimization through sets and functions, covering intersections, examples, operations, gradient, Hessian, and real-world applications.

Geodesic Convexity: Theory and Applications

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

Curvilinear Integrals: Interpretation and Convexity

Explores the interpretation of curvilinear integrals in vector fields and the proof of potential fields.

Optimization Techniques: Convexity in Machine Learning

Covers optimization techniques in machine learning, focusing on convexity and its implications for efficient problem-solving.

Minkowski-Weyl: Convexity and Separation Theorem

Explores convex sets, Minkowski-Weyl theorem, and Separation theorem in convex analysis.

Optimization Basics: Norms, Convexity, Differentiability

Explores optimization basics such as norms, convexity, and differentiability, along with practical applications and convergence rates.

Convex Sets and Functions

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