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MGT-418: Convex optimization

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Lectures in this course (76)

Lyapunov Stability in Dynamical Systems Log in to Mediaspace to watch this video

Covers Lyapunov stability in dynamical systems, focusing on global asymptotic stability and practical implementation through semidefinite programming.

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

Explores epigraphs, convexity of bivariate functions, and log-sum-exp functions in convex optimization.

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

Explores the theory and applications of convex optimization, covering topics such as log-determinant function, affine transformations, and relative entropy.

Convexity of Sum of Inverse Eigenvalues Log in to Mediaspace to watch this video

Covers the convexity proof of the sum of the eigenvalues of the inverse matrix.

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

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

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: Generalized Inequalities Log in to Mediaspace to watch this video

Explores problems with generalized inequalities in convex optimization and the equivalence between SOCP and SDP.

Convex Optimization: Self-dual Cones Log in to Mediaspace to watch this video

Explores self-dual cones in convex optimization and their applications in various optimization problems.

Convex Sets: Mathematical Optimization Log in to Mediaspace to watch this video

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

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

Provides a review of linear algebra concepts crucial for convex optimization, covering topics such as vector norms, eigenvalues, and positive semidefinite matrices.

Lagrangian Duality: Optimization Tutorial Log in to Mediaspace to watch this video

Covers Lagrangian duality in optimization, focusing on the minimum bin path problem and path time optimization.

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

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

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

Explores KKT conditions in convex optimization, covering dual problems, logarithmic constraints, least squares, matrix functions, and suboptimality of covering ellipsoids.

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.

Optimization in Statistics and Machine Learning: Maximum Likelihood Estimation Log in to Mediaspace to watch this video

Explores Maximum Likelihood Estimation, linear models, logistic regression, and Support Vector Machines.

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

Explores convex optimization theory, covering convex sets, functions, and QCQP duality.

Convexifying Nonconvex Problems: MGT-418 Lecture Log in to Mediaspace to watch this video

Explores convexifying nonconvex problems through kernel tricks, sensitivity interpretation, and nonlinear dimensionality reduction.

Learning the Kernel: Convex Optimization Log in to Mediaspace to watch this video

Explores learning the kernel function in convex optimization, focusing on predicting outputs using a linear classifier and selecting optimal kernel functions through cross-validation.

Convexifying Nonconvex Problems: SDP and SOCP Relaxations Log in to Mediaspace to watch this video

Explores convexifying nonconvex problems using SDP and SOCP relaxations in the context of optimal power flow.

Image Denoising: Formulation and Key Concepts Log in to Mediaspace to watch this video

Covers the process of image denoising and introduces key concepts for the first black hole image.

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