Optimization Basics: Linear Algebra, Analysis, Convexity

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

Explores convexity, Jacobians, subdifferentials, and convergence rates in optimization and function analysis.

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

Covers matrix norms, including the spectral and Frobenius norms.

Introduces Convex Optimization notation, convex functions, vector norms, and matrix properties.

Explores orthogonal matrices and transformations, emphasizing preservation of norms and angles.

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

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

Covers faster gradient descent methods and projected gradient descent for constrained optimization in machine learning.

Introduces Fenchel conjugation, exploring its properties, examples, and applications in nonsmooth optimization problems and minimax formulations.