# Regular point

### From Glossary

This pertains to a mathematical program whose functions are in and the issue is whether the Lagrange Multiplier Rule is valid. A ** regular point** is a point that satisfies some constraint qualification, but some authors are more specific and require the

*Lagrange constraint qualification*:

- Let denote the matrix whose rows are the gradients of all active constraints. Then, is a
*regular point*if has full row rank.

This gives additional properties (e.g., see the tangent plane).

In this context, a regular point is also called *Lagrange regular*. The mathematical program is [Lagrange] regular if every feasible point is [Lagrange] regular.