Introduction to Nonlinear Optimization

This course extends the optimization toolkit beyond linear programming to problems where objectives or constraints curve, with a heavy emphasis on convexity as the dividing line between problems you can actually solve and ones you can only approximate. You'll work through optimality conditions for unconstrained problems, then build up to KKT conditions and duality for constrained ones, mostly via problem sets where you derive conditions by hand and verify them on small examples, often in MATLAB following Beck's textbook. It sits downstream of IE 202 (linear optimization) and calculus, and feeds directly into machine learning, operations research, and any graduate work involving convex analysis — the KKT and duality machinery here is what later courses assume you already know.