Convex Optimization: The Big Picture | Least Squares, Linear Programming & Why Convexity Matters

Chapters: 0:00 Convex optimization: the big picture 0:32 What is an optimization problem? 1:49 Feasible and optimal 2:36 Where optimization problems come from 3:31 Most problems are hard 4:22 Linear functions 5:20 Convex functions 6:35 Convex is more general than linear 7:23 Least squares 8:37 Expanding the objective 9:53 The normal equations 11:12 A second proof, without derivatives 12:11 Least squares in practice 13:25 Linear programming 14:38 A trick: Chebyshev approximation as an LP 15:59 Convex optimization problems 17:07 Nonlinear optimization: local and global 18:17 Why convexity is the dividing line 19:37 Convex optimization inside nonconvex problems 20:30 The road ahead 21:16 Notation for the course 22:14 Recap