Lectures related to Optimal Transport: Gradient Flows in Rd

KKT and Convex Optimization

Covers the KKT conditions and convex optimization, discussing constraint qualifications and tangent cones of convex sets.

Convex Optimization: Sets and Functions

Introduces convex optimization through sets and functions, covering intersections, examples, operations, gradient, Hessian, and real-world applications.

Banach Spaces: Reflexivity and Convergence

Explores Banach spaces, emphasizing reflexivity and sequence convergence in a rigorous mathematical framework.

High Order Methods: Space Discretisation

Covers high order methods for space discretisation in linear differential systems.

Optimal Transport: Gradient Flows

Explores optimal transport, gradient flows, the implicit Euler scheme, and the heat equation in the context of Dirichlet energy functional.

Error Estimation in Numerical Methods

Explores error estimation in numerical methods for solving ordinary differential equations, emphasizing the impact of errors on solution accuracy and stability.

Convex Sets: Theory and Applications

Explores convex sets, their properties, and applications in optimization.

Abstract Variational Problems

Covers abstract variational problems in Hilbert spaces, focusing on boundedness, continuity, and coercivity.