Fenchel Conjugation: Basics and Applications

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Mathematics of Data: Optimization Basics

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

Normed Spaces

Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.

Conjugate Duality: Understanding Convex Optimization

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

Optimal Transport: Rockafellar Theorem

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

Linear Algebra Review: Convex Optimization

Covers essential linear algebra concepts for convex optimization, including vector norms, eigenvalue decomposition, and matrix properties.

Convex Optimization: Sets and Functions

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

Mathematics of Data: Optimization Basics

Covers optimization basics, including metrics, norms, convexity, gradients, and logistic regression, with a focus on strong convexity and convergence rates.

Convex Optimization: Gradient Descent

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

Optimization Techniques: Convexity in Machine Learning

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

Convex Optimization: Elementary Results

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