Lectures related to Convexity: Functions and Global Minima

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

Covers the properties and operations of convex functions.

Geodesic Convexity: Theory and Applications

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

KKT and Convex Optimization

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

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.

Convex Optimization: Convex Functions

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

Convex Optimization: Gradient Descent

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

Convex Optimization: Elementary Results

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

Geodesic convexity: why, and what we need

Explores geodesic convexity and its extension to optimization on manifolds, emphasizing the preservation of the key fact that local minima imply global minima.

Proximal Gradient Descent: Optimization Techniques in Machine Learning

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

Proximal and Subgradient Descent: Optimization Techniques

Discusses proximal and subgradient descent methods for optimization in machine learning.

Optimization Basics: Norms, Convexity, Differentiability

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

Mathematics of Data: Optimization Basics

Covers basics on optimization, including norms, Lipschitz continuity, and convexity concepts.

Convex Optimization: Sets and Functions

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

Convex Sets and Functions

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

Distributions and Derivatives

Covers distributions, derivatives, convergence, and continuity criteria in function spaces.

Fields Deriving from a Potential

Explores fields deriving from a potential, emphasizing integral and linear aspects.

Faster and Projected Gradient Descent: Optimization Techniques

Discusses advanced optimization techniques, focusing on faster and projected gradient descent methods in machine learning.

Optimization Techniques: Convexity in Machine Learning

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

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.