Optimal Transport: Cyclically Monotone Sets

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

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

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

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

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

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

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

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

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

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