Expectation Value and Convex Functions

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Proximal and Subgradient Descent: Optimization Techniques

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

K-means and Gaussian Mixture Model

Introduces K-means clustering, the Gaussian mixture model, Jensen's inequality, and the EM algorithm.

KKT and Convex Optimization

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

Optimization Basics: Norms, Convexity, Differentiability

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

Convex Functions: Theory and Applications

Explores convex functions, affine transformations, pointwise maximum, minimization, Schur's Lemma, and relative entropy in mathematical optimization.

Convex Optimization: Gradient Flow

Explores convex optimization, emphasizing the importance of minimizing functions within a convex set and the significance of continuous processes in studying convergence rates.

Optimal Transport: Gradient Flows in Rd

Explores optimal transport and gradient flows in Rd, emphasizing convergence and the role of Lipschitz and Picard-Lindelöf theorems.

Optimization Basics

Introduces optimization basics, covering logistic regression, derivatives, convex functions, gradient descent, and second-order methods.