linear-programming
2 free lessons tagged linear-programming across Math. Each one is a short sequence of focused steps with narration and a five-question quiz at the end — take them in any order, no signup required.
Newton's method and the interior point revolution
Second derivatives buy something gradients cannot: a step shaped by curvature, immune to conditioning, converging quadratically. This lesson builds Newton's method, then layers it on a log barrier to get interior point methods, the machinery that made large constrained problems solvable with a certificate rather than a hope.
Lagrangian Duality: From Primal to Dual
Every constrained optimization problem has a twin. Learn how to build the Lagrangian, derive the dual problem, and use weak duality, strong duality, and the KKT conditions to certify optima — with worked examples from linear programming and SVMs.