Lectures related to Optimal Transport: Cyclically Monotone Sets

Covers the properties and operations of convex functions.

Explores the Rockafellar Theorem in optimal transport, focusing on c-cyclical monotonicity and convex functions.

Geodesic Convexity: Theory and Applications

Explores geodesic convexity in metric spaces and its applications, discussing properties and the stability of inequalities.

Functions: Definitions and Notations

Covers the generalities of functions, including the definition of an application between sets and the uniqueness of elements in the image set.

Mathematical Analysis: Functions and Composition

Covers the analysis of functions, composition, and mathematical induction.

Restriction, Prolongement et Graphe d'une Fonction

Explains the relationship between two functions through restriction and prolongation, emphasizing the importance of defining a function by its graph.

Sparsest Cut: ARV Theorem

Covers the proof of the Bourgain's ARV Theorem, focusing on the finite set of points in a semi-metric space and the application of the ARV algorithm to find the sparsest cut in a graph.

Composition of Applications in Mathematics

Explores the composition of applications in mathematics and the importance of understanding their properties.

Approximation Algorithms

Covers approximation algorithms for optimization problems, LP relaxation, and randomized rounding techniques.

Riemann Integral: Subdivisions and Volumes

Covers the concept of Riemann integral and volume calculation of closed pavements.

Optimal Transport: Theory and Applications

Explores Lagrange multipliers, minimax theorems, and convex subsets in optimal transport theory.

Constrained optimization: the basics

Covers the basics of constrained optimization, including tangent directions, trust-region subproblems, and necessary optimality conditions.

Introduction to Convexity

Introduces the key concepts of convexity and its applications in different fields.

Mapping Functions and Surjections

Explores mapping functions, surjections, injective and surjective functions, and bijective functions.

Graphical Definition: Level Sets and Domains

Covers the graphical definition of functions, focusing on level sets and domains.

Convex Optimization: Gradient Descent

Explores VC dimension, gradient descent, convex sets, and Lipschitz functions in convex optimization.

Convexity: Functions and Global Minima

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

Cartesian Product and Induction

Introduces Cartesian product and induction for proofs using integers and sets.

Proofs: Logic, Mathematics & Algorithms

Explores proof concepts, techniques, and applications in logic, mathematics, and algorithms.

Unconstrained Optimization Theory

Explores unconstrained optimization theory, covering global and local minima, convexity, and gradient concepts.