Lectures in course MGT-418: Convex optimization

Convex Optimization: Introduction and Sets Log in to Mediaspace to watch this video

Covers the fundamentals of convex optimization, including mathematical problems, minimizers, and solution concepts, with an emphasis on efficient methods and practical applications.

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.

Convex Optimization: Dual Cones Log in to Mediaspace to watch this video

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

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

Covers exercises related to convex optimization, including SOCP dual, KKT conditions, and equality constrained least squares.

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

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

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

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

Maximum Likelihood Estimation: Linear Models Log in to Mediaspace to watch this video

Explores maximum likelihood estimation in linear models, covering Gaussian noise, covariance estimation, and support vector machines for classification problems.

Convex Optimization: Farkas' Lemma Log in to Mediaspace to watch this video

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

Convex Optimization: Nonlinear Dimensionality Reduction Log in to Mediaspace to watch this video

Explores convex optimization in nonlinear dimensionality reduction, showcasing practical applications in signal processing and regression tasks.

Quantile Regression: Electricity Price Prediction Log in to Mediaspace to watch this video

Explores quantile regression for electricity price prediction using time series data, regularization, and the kernel trick.

Optimal Power Flow: Constraints and Relaxations Log in to Mediaspace to watch this video

Covers the Optimal Power Flow problem in power systems, focusing on constraints and relaxation methods to efficiently solve the nonconvex QCQP.

Quantile Regression: Linear Optimization Log in to Mediaspace to watch this video

Covers quantile regression, focusing on linear optimization for predicting outputs and discussing sensitivity to outliers, problem formulation, and practical implementation.

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.

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

Explores polynomial optimization, emphasizing sum-of-squares polynomials and their applications, including monomial representation and theorem proofs.

Image Denoising and Reconstruction Log in to Mediaspace to watch this video

Covers denoising and reconstructing images using total variation minimization and discusses the visual effects of different regularization strengths.

Polynomial Optimization: SOS and SDP Log in to Mediaspace to watch this video

Explores Sum of Squares polynomials and Semidefinite Programming in Polynomial Optimization, enabling the approximation of non-convex polynomials with convex SDP.

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.

Robust Optimization in Radiation Therapy Log in to Mediaspace to watch this video

Explores robust optimization in radiation therapy, emphasizing dose optimization and trade-offs between nominal and robust solutions.

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

Covers Distributionally Robust Portfolio Optimization for maximizing expected utility with uncertain asset returns.

Portfolio Optimization: Models and Strategies Log in to Mediaspace to watch this video

Explores portfolio optimization models and strategies under uncertainty, emphasizing decision criteria like value-at-risk and mean-variance functional.