Convexifying Nonconvex Problems: MGT-418 Lecture

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Legendre Transform

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

Optimization Techniques: Convexity and Algorithms in Machine Learning

Covers optimization techniques in machine learning, focusing on convexity, algorithms, and their applications in ensuring efficient convergence to global minima.

KKT and Convex Optimization

Covers the KKT conditions and convex optimization, discussing constraint qualifications and tangent cones of convex sets.

Convex Optimization

Introduces convex optimization, focusing on the importance of convexity in algorithms and optimization problems.

Convex Optimization: Introduction and Sets

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

Convex Optimization: Dual Cones

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

Image Denoising and Reconstruction

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

Convex Optimization: Nonlinear Dimensionality Reduction

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

The Hidden Convex Optimization Landscape of Deep Neural Networks

Explores the hidden convex optimization landscape of deep neural networks, showcasing the transition from non-convex to convex models.

Optimization Techniques: Stochastic Gradient Descent and Beyond

Discusses optimization techniques in machine learning, focusing on stochastic gradient descent and its applications in constrained and non-convex problems.