Definition:Binding Constraint

Definition

Let $\RR$ be a weak inequality on some set $S$.

Let $a \mathrel \RR b$ be a constraint given by a weak inequality $\RR$.

Let $P \in S$ such that $P \mathrel \RR b$ is an equality.

Then $a \mathrel \RR b$ is binding at $P$.

Also known as

A binding constraint is also known as an active constraint.

Examples

Example: $x^2 + y^2 \le 2$

Consider the weak inequality:

$x^2 + y^2 \le 2$

Consider the point $\tuple {x, y} = \tuple {1, 1}$.

Then the constraint $x^2 + y^2 \le 2$ is binding at $\tuple {1, 1}$, as $1^2 + 1^2 = 2$.

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): active (of a constraint)
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): binding or active