Structured Sparsity: Atomic Norms and Convex Optimization

This lecture covers the concept of atomic norms, gauge functions, and their application in convex optimization problems. It discusses the mathematical foundations of atomic norms, their relationship with convex hulls, and their extension to various regularizers. The lecture also explores the use of atomic norms in solving regularized least-squares problems, multi-knapsack feasibility problems, and matrix completion. Additionally, it delves into structured sparsity, highlighting different non-smooth regularizers like group sparsity and tree sparsity. The lecture concludes with discussions on parameter selection, non-smooth convex minimization, subdifferentials, and stochastic subgradient methods.