Optimal Transport: Convexity and Inequalities

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Initial Problem Solutions Log in to Mediaspace to watch this video

Covers the description of all solutions of the initial problem and related concepts such as compactness and closure.

Convex Optimization: Elementary Results Log in to Mediaspace to watch this video

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

Conjugate Duality: Understanding Convex Optimization Log in to Mediaspace to watch this video

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

Minkowski's Theorems: Lattices and Volumes Log in to Mediaspace to watch this video

Explores Minkowski's theorems on lattices, volumes, and set comparisons.

Optimization Techniques: Gradient Descent and Convex Functions Log in to Mediaspace to watch this video

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

Convex Optimization: Sets and Functions Log in to Mediaspace to watch this video

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Proximal Gradient Descent: Optimization Techniques in Machine Learning Log in to Mediaspace to watch this video

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Convex Functions Log in to Mediaspace to watch this video

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Compact Sets and Extreme Values Log in to Mediaspace to watch this video

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Isoperimetric Inequality: Optimal Transport Log in to Mediaspace to watch this video

Explores the isoperimetric inequality and its application in optimal transport, discussing properties of optimal maps and quality cases.

Linear Operations: Convergence and Sequences Log in to Mediaspace to watch this video

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Sparsest Cut: ARV Theorem Log in to Mediaspace to watch this video

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Convergence of Fourier Series Log in to Mediaspace to watch this video

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Untitled Log in to Mediaspace to watch this video

Cauchy-Lipschitz Theorem: Examples and Applications Log in to Mediaspace to watch this video

Explores examples and applications of the Cauchy-Lipschitz theorem in sequences and Banach spaces.

Orthogonality: Norm, Scalar Product, Perpendicularity Log in to Mediaspace to watch this video

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