Lectures related to Expectation Value and Convex Functions

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

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

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

Convexity: Functions and Global Minima

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

Convex Optimization: Convex Functions

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

Convex Sets and Functions

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

Geodesic Convexity: Theory and Applications

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

Convex Optimization: Elementary Results

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

Basic Properties of Conditional Expectation

Covers basic properties of conditional expectation and Jensen's inequality in probability theory.

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.

Convex Functions

Covers the properties and operations of convex functions.

Optimization Problems: Path Finding and Portfolio Allocation

Covers optimization problems in path finding and portfolio allocation.

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

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

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.

Proximal Gradient Descent: Optimization Techniques in Machine Learning

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

Mathematics of Data: Optimization Basics

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

Convex Functions: Theory and Applications

Introduces convex functions, covering affine, convex, and conic hulls, transformations, inequalities, and conditions for convexity.