Geodesic Convexity: Theory and Applications

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Convex Sets: Theory and Applications

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

Conjugate Duality: Understanding Convex Optimization

Explores conjugate duality in convex optimization, covering weak and supporting hyperplanes, subgradients, duality gap, and strong duality conditions.

Optimization Techniques: Gradient Descent and Convex Functions

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

Optimal Transport: Regularity and Brenier's Theorem

Explores optimal transport regularity and Brenier's theorem, discussing continuity and convexity concepts.

Convex Optimization: Sets and Functions

Introduces convex optimization through sets and functions, covering intersections, examples, operations, gradient, Hessian, and real-world applications.

Preliminaries in Measure Theory

Covers the preliminaries in measure theory, including loc comp, separable, complete metric space, and tightness concepts.

Correlations of the Liouville function

Explores correlations of the Liouville function along deterministic and independent sequences, covering key concepts and theorems.

Cones of convex sets

Explores optimization on convex sets, including KKT points and tangent cones.

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