Optimal Transport: Analysis and Proofs

Related lectures (40)

Covers extreme points, compact intervals, and optimization problems in analysis.

Explores distribution and interpolation spaces, showcasing their importance in mathematical analysis and the computations involved.

Covers the proof of the existence of y and the resolution of EDOs with practical examples.

Covers the conditions for finding absolute extrema in multivariable functions.

Explores continuity and limits, emphasizing their relationship and practical applications in function analysis.

Covers the Implicit Functions Theorem, providing a general understanding of implicit functions.

Explores real functions, covering parity, periodicity, and polynomial functions.

Covers weak derivatives, their properties, and applications in functional analysis.

Covers the properties of harmonic functions and the concept of mollification.

Explores limits, continuity, and uniform continuity in functions, including properties at specific points and closed intervals.

Discusses center of gravity, variable change, spherical coordinates, and bijectivity in mathematical analysis.

Covers the properties of the Laplace transform and its applications.

Explores the Fourier transformation on L^2, emphasizing convergence and density in Fourier analysis.

Covers optimization algorithms, convergence properties, and time complexity of sequences and functions.

Explores the construction and properties of CW complexes, focusing on characteristic maps, closed subsets, products, quotients, and cell formation.

Covers exercises on convex optimization, focusing on formulating and solving optimization problems using YALMIP and solvers like GUROBI and MOSEK.

Covers vector spaces, compact sets, convergence, continuity, and uniqueness theorems.

Explores the Cauchy-Lipschitz theorem for local existence and uniqueness of solutions to differential equations.

Covers convergence criteria, properties of sequences, and the Achilles Paradox.

Explores the classification of PDEs into linear, semi-linear, and quasi-linear types, emphasizing the properties of their solutions.

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