View source for Active constraint

Let be given a constrained optimization problem

maximize <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a110/a110260/a1102601.png" />, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a110/a110260/a1102602.png" />,

subject to <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a110/a110260/a1102603.png" />, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a110/a110260/a1102604.png" />.

The <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a110/a110260/a1102605.png" />th constraint is said to be active (at a solution <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a110/a110260/a1102606.png" />) if <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a110/a110260/a1102607.png" />.

See also [[Passive constraint|Passive constraint]]. For a selection of references, see [[Mathematical programming|Mathematical programming]].