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Lecture
Convex Functions: Elementary Concepts
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Related lectures (30)
Introduction to Convexity
Introduces the key concepts of convexity and its applications in different fields.
Optimization Techniques: Convexity in Machine Learning
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Convex Sets and Functions
Introduces convex sets and functions, discussing minimizers, optimality conditions, and characterizations, along with examples and key inequalities.
Subgradients and Convex Functions
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Convex Optimization: Elementary Results
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Explores elementary results in convex optimization, including affine, convex, and conic hulls, proper cones, and convex functions.
Convex Functions: Theory and Applications
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Introduces convex functions, covering affine, convex, and conic hulls, transformations, inequalities, and conditions for convexity.
Optimal Transport: Rockafellar Theorem
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Explores the Rockafellar Theorem in optimal transport, focusing on c-cyclical monotonicity and convex functions.
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.
Convex Functions: Theory and Applications
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Explores convex functions, affine transformations, pointwise maximum, minimization, Schur's Lemma, and relative entropy in mathematical optimization.
Convex Functions: Theory and Applications
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Explores convex functions, including checking convexity, transformations, examples, minimization, geometric intuition, Schur's Lemma, distance function, perspective function, and relative entropy.
Convex Optimization: Sets and Functions
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Introduces convex optimization through sets and functions, covering intersections, examples, operations, gradient, Hessian, and real-world applications.
Convex Optimization
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Introduces convex optimization, focusing on the importance of convexity in algorithms and optimization problems.
Convexity: Functions and Global Minima
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Explores convex functions, global minima, and their relationship with differentiability.
KKT and Convex Optimization
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Covers the KKT conditions and convex optimization, discussing constraint qualifications and tangent cones of convex sets.
Conjugate Duality: Understanding Convex Optimization
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Explores conjugate duality in convex optimization, covering weak and supporting hyperplanes, subgradients, duality gap, and strong duality conditions.
Optimization Techniques: Convexity and Algorithms in Machine Learning
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Covers optimization techniques in machine learning, focusing on convexity, algorithms, and their applications in ensuring efficient convergence to global minima.
Optimization Techniques: Gradient Descent and Convex Functions
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Provides an overview of optimization techniques, focusing on gradient descent and properties of convex functions in machine learning.
Convex Optimization: Gradient Descent
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Explores VC dimension, gradient descent, convex sets, and Lipschitz functions in convex optimization.
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