Lectures related to Jensen's Inequality

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

Geodesic Convexity: Theory and Applications

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

Convex Optimization: Convex Functions

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

Convex Functions

Covers the definition of convex functions and their properties in optimization.

Convex Functions

Covers the properties and operations of convex functions.

Introduction to Convexity

Introduces the key concepts of convexity and its applications in different fields.

Convexity: Functions and Global Minima

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

Convex Optimization: Elementary Results

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

Optimization Techniques: Convexity in Machine Learning

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

Convex Optimization: Sets and Functions

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

Conjugate Duality: Understanding Convex Optimization

Explores conjugate duality in convex optimization, covering weak and supporting hyperplanes, subgradients, duality gap, and strong duality conditions.

Convex Optimization: Gradient Descent

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

Optimal Transport: Convexity and Inequalities

Explores optimal transport, emphasizing convexity properties and inequalities in compact sets.

Convex Optimization

Introduces convex optimization, focusing on the importance of convexity in algorithms and optimization problems.

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.

KKT and Convex Optimization

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

Proximal Gradient Descent: Optimization Techniques in Machine Learning

Discusses proximal gradient descent and its applications in optimizing machine learning algorithms.

Convex Sets and Functions

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

Subgradients and Convex Functions

Explores subgradients in convex functions, emphasizing non-differentiable yet convex scenarios and properties of subdifferentials.

Optimization Techniques: Gradient Descent and Convex Functions

Provides an overview of optimization techniques, focusing on gradient descent and properties of convex functions in machine learning.