Convex Optimization: Generalized Inequalities

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Conjugate Duality: Envelope Representations and Subgradients Log in to Mediaspace to watch this video

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

Conjugate Duality: Understanding Convex Optimization Log in to Mediaspace to watch this video

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

Legendre Transform Log in to Mediaspace to watch this video

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

Distributionally Robust Portfolio Optimization Log in to Mediaspace to watch this video

Explores distributionally robust portfolio optimization and compares different estimation approaches and methods for portfolio evaluation.

Convex Optimization: Elementary Results Log in to Mediaspace to watch this video

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

Convex Optimization Log in to Mediaspace to watch this video

Covers an overview of convex optimization, affine sets, polyhedra, ellipsoids, and convex functions.

Optimization Problems: Standard Form Log in to Mediaspace to watch this video

Explores optimization problems in standard form, convex optimization, and optimality criteria.

Linear Algebra Review: Convex Optimization Log in to Mediaspace to watch this video

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

Support Vector Regression: Recap and Convex Optimization Log in to Mediaspace to watch this video

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

Convex Optimization: Exercises Log in to Mediaspace to watch this video

Covers exercises on convex optimization, focusing on formulating and solving optimization problems using YALMIP and solvers like GUROBI and MOSEK.

Convex Optimization: Duality and KKT Conditions Log in to Mediaspace to watch this video

Explores convex optimization duality, KKT conditions, and financial arbitrage detection.

Lyapunov Stability: Convex Optimization Log in to Mediaspace to watch this video

Covers Lyapunov stability in convex optimization and its implementation through trajectory plots.

Convex Optimization: Theory and Applications Log in to Mediaspace to watch this video

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

Optimal Transport: Theory and Applications Log in to Mediaspace to watch this video

Covers the theory and applications of optimal transport, focusing on infimal convolution and Kantorovich potentials.

Solving Linear Programs: SIMPLEX Method Log in to Mediaspace to watch this video

Explains the SIMPLEX method for solving linear programs and optimizing the solution through basis variable manipulation.

General Conics and Homogeneous Coordinates Log in to Mediaspace to watch this video

Covers general conics, homogeneous coordinates, conic recognition, and matrix decomposition.

Introduction to Shortest Path Log in to Mediaspace to watch this video

Introduces the concept of shortest path, discussing weighted paths, Hamiltonian paths, and path optimization algorithms.

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