Convex Optimization: Convex Functions

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Convex Functions

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

Conjugate Duality: Understanding Convex Optimization

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

Geodesic Convexity: Basic Definitions

Introduces geodesic convexity on Riemannian manifolds and explores its properties.

Optimization with Constraints: KKT Conditions

Covers the KKT conditions for optimization with constraints, essential for solving constrained optimization problems efficiently.

Conjugate Duality: Envelope Representations and Subgradients

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

Convex Optimization

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

Optimization Methods: Convergence and Trade-offs

Covers optimization methods, convergence guarantees, trade-offs, and variance reduction techniques in numerical optimization.

Geodesically Convex Optimization

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

Linear Independence: The Wronskian Concept

Explains the Wronskian and its role in determining linear independence of solutions to differential equations.