MGT-418: Convex optimization

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Lectures in this course (76)

Convex Optimization: Convex Functions

Covers the concept of convex functions and their applications in optimization problems.

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KKT Conditions: Convex Optimization

Explores KKT conditions in convex optimization, covering dual cones, properties, generalized inequalities, and optimality conditions.

Convexity of Sum of Inverse Eigenvalues

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

Convex Optimization Problems: Standard Form

Covers convex optimization problems, transformation to standard form, and optimality criteria for differentiable objectives.

Conjugate Duality: Envelope Representations and Subgradients

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

Optimization Problems: Standard Form

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

Convex Optimization: Exercises

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

Convex Optimization Problems

Covers Convex Optimization Problems, LP formulations, and practical implementations using CVXPY and GUROBI.

Optimization in Statistics and Machine Learning: Maximum Likelihood Estimation

Explores maximum likelihood estimation, logistic regression, covariance estimation, and support vector machines for classification problems.

Convexifying Nonconvex Problems: SVM and Dimensionality Reduction

Explores convexifying nonconvex problems through SVM and dimensionality reduction techniques.

Convex Optimization: Generalized Inequalities

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

Convex Optimization: Yalmip Introduction

Introduces Yalmip, a MATLAB toolbox for optimization modeling and solving with MOSEK and GUROBI.

Lagrangian Duality: Convex Optimization

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

Convex Relaxation in Optimization

Explores convexifying nonconvex problems through relaxation techniques, illustrated with total variation reconstruction examples.

Convex Optimization: Self-dual Cones

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

Max-Cut Problem: SDP Relaxation and Randomized Rounding

Explores the Max-Cut Problem, its relaxation using SDP, and Polynomial Optimization.

Convex Optimization: Dual Cones

Explores dual cones, generalized inequalities, SDP duality, and KKT conditions in convex optimization.

Lagrangian Duality: Optimization Tutorial

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

Robust Optimization: Polynomial Approximation & Uncertainty Sets

Explores robust optimization through polynomial approximation and uncertainty sets, including robust linear programs and optimization tricks.

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