Convex Optimization: Theory and Applications

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Related lectures (29)

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Convex Optimization: Gradient Descent

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

KKT Conditions: Convex Optimization

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

KKT for convex problems and Slater's CQ

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

Optimization Problems: Path Finding and Portfolio Allocation

Covers optimization problems in path finding and portfolio allocation.

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.

Support Vector Regression: Recap and Convex Optimization

Covers the recap of Support Vector Regression with a focus on convex optimization and its equivalence to Gaussian Process Regression.

Conjugate Duality: Envelope Representations and Subgradients

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

Geodesic Convexity: Theory and Applications

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

Legendre Transform

Explores the Legendre transform, duality in convex analysis, and optimization problems.