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Lecture
Geodesic Convexity: Basic Definitions
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Related lectures (48)
Geodesic Convexity: Basic Facts and Definitions
Explores geodesic convexity, focusing on properties of convex functions on manifolds.
Differential Forms on Manifolds
Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.
Optimization on Manifolds: Context and Applications
MOOC: Introduction to optimization on smooth manifolds: first order methods
Introduces optimization on manifolds, covering classical and modern techniques in the field.
Convexity and Jacobians
Explores convexity, Jacobians, subdifferentials, and convergence rates in optimization and function analysis.
Optimization Basics: Norms, Convexity, Differentiability
Explores optimization basics such as norms, convexity, and differentiability, along with practical applications and convergence rates.
Convex Functions: Theorems and Examples
Discusses the theorems on convex functions and provides examples for better understanding.
Trust Region Methods: Why, with an Example
Introduces trust region methods and presents an example of Max-Cut Burer-Monteiro rank 2 optimization.
Local Extrema of Functions
Discusses local extrema of functions in two variables around the point (0,0).
Linear convergence with Polyak-Łojasiewicz: Mechanical proof
Explores linear convergence with the Polyak-Łojasiewicz condition on a Riemannian manifold.
Optimality Conditions: First Order
MOOC: Introduction to optimization on smooth manifolds: first order methods
Covers optimality conditions in optimization on manifolds, focusing on global and local minimum points.
Dynamics of Steady Euler Flows: New Results
Explores the dynamics of steady Euler flows on Riemannian manifolds, covering ideal fluids, Euler equations, Eulerisable flows, and obstructions to exhibiting plugs.
Taylor's Formula: Developments and Extrema
Covers Taylor's formula, developments, and extrema of functions, discussing convexity and concavity.
Bernoulli's Hospital Rule
MOOC: Analysis I
MOOC: Analysis I (part 6) : Study of functions, limited developments
Covers the statement of the Bernoulli's Hospital Rule and its application.
Morse Theory: Critical Points and Non-Degeneracy
Covers Morse theory, focusing on critical points and non-degeneracy.
Integral Techniques: Integration by Parts
Explores the integration by parts technique through examples, showcasing its step-by-step application to functions like cos(x) and sin(x.
Convex Functions
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Covers the properties and operations of convex functions.
Riemannian distance, geodesically convex sets
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Covers the structure of Riemannian manifolds, geodesic convexity, and the Riemannian distance function.
Geodesically Convex Optimization
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Covers geodesically convex optimization on Riemannian manifolds, exploring convexity properties and minimization relationships.
Convex Optimization: Convex Functions
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Covers the concept of convex functions and their applications in optimization problems.
Geodesic Convexity: Theory and Applications
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Explores geodesic convexity in metric spaces and its applications, discussing properties and the stability of inequalities.
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