Optimization & Machine Learning
M16 — Fall 24
Contents
1 Introduction
2 Fundamentals
2.1 Global and local extrema of functions
2.2 Critical points
2.3 Convexity and concavity
2.4 Simple optimization problems
3 Constrained optimization using Lagrange multipliers
3.1 Lagrange multipliers
3.2 Lagrange multipliers with multiple equality constraints
3.3 Lagrange multiplier theorem
3.4 Lagrangian function and dual optimization problem
3.5 Primal-dual optimality and KKT conditions with only equality constraints
3.6 Inequality constraints
4 Numerical optimization algorithms
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