Convex Optimization: Convex Functions

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Related lectures (46)

Convex Functions Log in to Mediaspace to watch this video

Covers the definition of convex functions and their properties in optimization.

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.

Conjugate Duality: Envelope Representations and Subgradients Log in to Mediaspace to watch this video

Explores envelope representations, subgradients, and the duality gap in convex optimization.

Convex Optimization Log in to Mediaspace to watch this video

Covers an overview of convex optimization, affine sets, polyhedra, ellipsoids, and convex functions.

Geodesically Convex Optimization Log in to Mediaspace to watch this video

Covers geodesically convex optimization on Riemannian manifolds, exploring convexity properties and minimization relationships.

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.

Optimal Transport: Rockafellar Theorem Log in to Mediaspace to watch this video

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

Python Complement: Numpy, Scipy, Matplotlib Log in to Mediaspace to watch this video

Covers advanced Python topics like numpy operations, scipy linear algebra, and matplotlib for creating figures.

Eigenvalues and Eigenvectors Log in to Mediaspace to watch this video

Covers eigenvalues and eigenvectors in linear algebra.

Fields Deriving from a Potential Log in to Mediaspace to watch this video

Explores fields deriving from a potential, emphasizing integral and linear aspects.

Convex Sets: Mathematical Optimization Log in to Mediaspace to watch this video

Introduces convex optimization, covering convex sets, solution concepts, and efficient numerical methods in mathematical optimization.

Explores matrix similarity, eigenvalues, and diagonalization in linear algebra.

Linear Algebra: Vector Spaces and Linear Independence Log in to Mediaspace to watch this video

Covers vector spaces, operations, and linear independence with examples from polynomials and functions.

Polynomial Characteristic and Eigenvalues Log in to Mediaspace to watch this video

Covers the concept of polynomial characteristic of a matrix and its relation to eigenvalues.

Truncated CG: Conjugate Gradients Log in to Mediaspace to watch this video

Covers the truncated conjugate gradients algorithm for solving positive definite linear maps iteratively.

Matrix Operations: Linear Forms and Bases Log in to Mediaspace to watch this video

Covers matrix operations, linear forms, and bases in mathematics, emphasizing their significance.

Linear Algebra: Spectral Decomposition Log in to Mediaspace to watch this video

Covers the spectral decomposition of matrices and change of basis applications.

Linear Algebra: Normal Equations and Symmetric Matrices Log in to Mediaspace to watch this video

Explores normal equations, pseudo-solutions, unique solutions, and symmetric matrices in linear algebra.

Spectral Theorem: Eigenvalues and Eigenvectors Log in to Mediaspace to watch this video

Covers the spectral theorem, eigenvalues, eigenvectors, and their importance in linear algebra.

Linear Algebra: Integers Log in to Mediaspace to watch this video

Explores linear algebra over integers, emphasizing solutions to A.x=b equations and Hermite normal form.

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