Separation Theorem: Convex Sets

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Covers Minbowski's Theorem on Diophantine Approximation and Gram-Schmidt orthogonalization.

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

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

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

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

Covers the concept of compact embedding in Banach spaces and Sobolev inequalities.

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

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

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

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