# Regular point

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This pertains to a mathematical program whose functions are in $LaTeX: C^1,$ 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 $LaTeX: G(x)$ denote the matrix whose rows are the gradients of all active constraints. Then, $LaTeX: x$ is a regular point if $LaTeX: G(x)$ 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.