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Difference between revisions of "Active constraint"

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Let be given a constrained optimization problem
 
Let be given a constrained optimization problem
  
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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" />,
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maximize $f(x)$, $x\in\mathbf R^n$,
  
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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" />.
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subject to $g_i(x)\leq0$, $i=1,\ldots,m$.
  
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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" />.
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The $i$th constraint is said to be active (at a solution $y$) if $g_i(y)=0$.
  
 
See also [[Passive constraint|Passive constraint]]. For a selection of references, see [[Mathematical programming|Mathematical programming]].
 
See also [[Passive constraint|Passive constraint]]. For a selection of references, see [[Mathematical programming|Mathematical programming]].

Revision as of 13:34, 25 April 2014

Let be given a constrained optimization problem

maximize $f(x)$, $x\in\mathbf R^n$,

subject to $g_i(x)\leq0$, $i=1,\ldots,m$.

The $i$th constraint is said to be active (at a solution $y$) if $g_i(y)=0$.

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

How to Cite This Entry:
Active constraint. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Active_constraint&oldid=14642
This article was adapted from an original article by M. Hazewinkel (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article
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