Introduction to Proximal Operators

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Convex Optimization: Examples of Convex Functions

Explores convex optimization, convex functions, and their properties, including strict convexity and strong convexity, as well as different types of convex functions like linear affine functions and norms.

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 Basics: Norms, Convexity, Differentiability

Explores optimization basics such as norms, convexity, and differentiability, along with practical applications and convergence rates.

Structured Sparsity: Atomic Norms and Convex Optimization

Explores atomic norms, convex optimization, and structured sparsity in mathematical data analysis.

Optimization Methods: Convexity and Gradient Descent

Explores optimization methods, including convexity, gradient descent, and non-convex minimization, with examples like maximum likelihood estimation and ridge regression.

From Stochastic Gradient Descent to Non-Smooth Optimization

Covers stochastic optimization, sparsity, and non-smooth minimization via subgradient descent.

KKT and Convex Optimization

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

Gradient Descent: Optimization Techniques

Explores gradient descent, loss functions, and optimization techniques in neural network training.

Sparse Regression

Covers the concept of sparse regression and the use of Gaussian additive noise in the context of MAP estimator and regularization.

Convex Functions

Covers the properties and operations of convex functions.