# Convex program

### From Glossary

The mathematical program is convex if the objective function is convex, and the feasible region is a convex set. In particular, the mathematical program is convex if
is convex, and is affine. See the supplement, Convex Cones, Sets, and Functions.

Here are some key properties of a convex program:

- Every local optimum is a global optimum.
- First-order conditions are sufficient.
- Lagrangian duality is strong.