Lecture

Convex Optimization

Related lectures (27)

Introduces convex optimization, focusing on the importance of convexity in algorithms and optimization problems.

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

Convex Optimization: Gradient Flow

Explores convex optimization, emphasizing the importance of minimizing functions within a convex set and the significance of continuous processes in studying convergence rates.

Subgradients and Convex Functions

Explores subgradients in convex functions, emphasizing non-differentiable yet convex scenarios and properties of subdifferentials.

Optimization Techniques: Convexity in Machine Learning

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

Convex Optimization: Theory and Applications

Explores convex optimization theory, covering local and global minima, convex functions, and applications in various fields.

Optimization Techniques: Convexity and Algorithms in Machine Learning

Covers optimization techniques in machine learning, focusing on convexity, algorithms, and their applications in ensuring efficient convergence to global minima.

The Hidden Convex Optimization Landscape of Deep Neural Networks

Explores the hidden convex optimization landscape of deep neural networks, showcasing the transition from non-convex to convex models.

Convex Optimization: Gradient Descent

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

Optimal Transport: Rockafellar Theorem

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

Linear Algebra Review: Convex Optimization

Covers essential linear algebra concepts for convex optimization, including vector norms, eigenvalue decomposition, and matrix properties.

KKT for convex problems and Slater's CQ

Covers the KKT conditions and Slater's condition in convex optimization problems.

Convex Optimization: Sets and Functions

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

Gradient Descent Methods: Theory and Computation

Explores gradient descent methods for smooth convex and non-convex problems, covering iterative strategies, convergence rates, and challenges in optimization.

Convex Optimization: Elementary Results

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

Convexity: Functions and Global Minima

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

Convex Optimization: Introduction and Sets

Covers the fundamentals of convex optimization, including mathematical problems, minimizers, and solution concepts, with an emphasis on efficient methods and practical applications.

Conjugate Duality: Understanding Convex Optimization

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

Conjugate Duality: Envelope Representations and Subgradients

Explores envelope representations, subgradients, and the duality gap in convex optimization.

Convex Sets: Mathematical Optimization

Introduces convex optimization, covering convex sets, solution concepts, and efficient numerical methods in mathematical optimization.