Convexity and Optimization for Economists

The course builds the ideas in order: convex sets, concave and quasi-concave functions, then unconstrained and constrained optimization by the Lagrangian method and the Kuhn–Tucker conditions. Calculus is assumed rather than taught here.

Assumed background: multivariable calculus, basic linear algebra.

Lessons

1. Convex sets The segment condition, the intersection property, and the convex sets optimization relies on.
2. Concave and convex functions Convexity carried from sets over to functions — the shapes that make maximisation and minimisation behave.

Offered self-paced.