Convex Optimization Problems

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Page 3 of 4

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

Convex Optimization

Introduces the fundamentals of convex optimization, emphasizing the significance of convex functions in simplifying the minimization process.

Convex Optimization: Elementary Results

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

Lagrangian Duality: Convex Optimization

Explores Lagrangian duality in convex optimization, transforming problems into min-max formulations and discussing the significance of dual solutions.

Convex Optimization: Farkas' Lemma

Covers Farkas' lemma, exploring the relationship between linear programs and the conditions for its validity.

Convex Optimization: Conjugate Duality

Explores envelope representations, subgradients, conjugate functions, duality gap, and strong duality in convex optimization.

Primal-dual Optimization III: Lagrangian Gradient Methods

Explores primal-dual optimization methods, emphasizing Lagrangian gradient techniques and their applications in data optimization.

Lagrangian Duality: Theory and Applications

Explores Lagrangian duality in convex optimization, discussing strong duality, dual solutions, and practical applications in second-order cone programs.

Optimization Techniques: Convexity in Machine Learning

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

KKT Conditions: Convex Optimization

Explores the KKT conditions in convex optimization, including dual cones, SDP duality, and convex hulls.