Optimal Transport: Gradient Flows in Rd

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Covers the semester project on numerics, focusing on adaptive algorithms and multistep methods.

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

Covers the concept of convex functions and their applications in optimization problems.

Explores convex functions, global minima, and their relationship with differentiability.

Explores numerical methods for solving ODE systems, stability regions, and absolute stability importance.

Explores zero-stability and absolute-stability in numerical methods, including Forward Euler, Backward Euler, Crank-Nicolson, and Heun's methods.

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

Explores weak convergence in Hilbert spaces, discussing definitions, implications, and examples.

Covers normed spaces, Banach spaces, and Hilbert spaces, as well as dual spaces and weak convergence.

Covers the representation of signals in vector spaces and inner product spaces, including the Projection Theorem.