Convex Sets and Functions

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Related lectures (29)

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Conjugate Duality: Understanding Convex Optimization

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

Gradient Descent: Principles and Applications

Covers gradient descent, its principles, applications, and convergence rates in optimization for machine learning.

Cones of convex sets

Explores optimization on convex sets, including KKT points and tangent cones.

Optimization Methods

Covers optimization methods without constraints, including gradient and line search in the quadratic case.

Expectation Value and Convex Functions

Explores expectation value, convex functions, weights, and inequalities in mathematical analysis.

Convex Functions: Theory and Applications

Explores convex functions, including checking convexity, transformations, examples, minimization, geometric intuition, Schur's Lemma, distance function, perspective function, and relative entropy.

Linear Algebra Review: Convex Optimization

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

Convex Optimization: Examples of Convex Functions

Explores convex optimization, convex functions, and their properties, including strict convexity and strong convexity, as well as different types of convex functions like linear affine functions and norms.

Mathematics of Data: Optimization Basics

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