Lectures related to Locally convex topological vector space

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

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

Covers the properties and operations of convex functions.

Geodesic Convexity: Theory and Applications

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

Cones of convex sets

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

Kirillov Paradigm for Heisenberg Group

Explores the Kirillov paradigm for the Heisenberg group and unitary representations.

Convex Optimization: Gradient Descent

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

Rigidity in Negative Curvature

Delves into the rigidity of negatively curved manifolds and the interplay between curvature and symmetry.

Convexity: Functions and Global Minima

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

KKT and Convex Optimization

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

Optimal Transport: Theory and Applications

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

Separation Theorem: Convex Sets

Explores the Second Separation Theorem for closed convex sets and the concept of supporting hyperplanes.

Convex Optimization: Elementary Results

Explores elementary results in convex optimization, including affine, convex, and conic hulls, proper cones, and convex functions.

Faster Gradient Descent: Projected Optimization Techniques

Covers faster gradient descent methods and projected gradient descent for constrained optimization in machine learning.

Optimization Techniques: Convexity in Machine Learning

Covers optimization techniques in machine learning, focusing on convexity and its implications for efficient problem-solving.

Mathematics of Data: Optimization Basics

Covers basics on optimization, including norms, Lipschitz continuity, and convexity concepts.

Convex Sets and Functions

Introduces convex sets and functions, discussing minimizers, optimality conditions, and characterizations, along with examples and key inequalities.

Convex Optimization: Sets and Functions

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

Curvilinear Integrals: Interpretation and Convexity

Explores the interpretation of curvilinear integrals in vector fields and the proof of potential fields.

Diophantine Approximation: Minbowski's Theorem

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