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Difference between revisions of "Passive constraint"

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''inactive constraint''
 
''inactive constraint''
  
 
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/p/p110/p110080/p1100801.png" />, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p110/p110080/p1100802.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/p/p110/p110080/p1100803.png" />, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p110/p110080/p1100804.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/p/p110/p110080/p1100805.png" />th constraint is said to be passive (at a solution <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p110/p110080/p1100806.png" />) if <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p110/p110080/p1100807.png" />.
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The $i$th constraint is said to be passive (at a solution $y$) if $g_i(y)<0$.
  
 
See also [[Active constraint|Active constraint]]. For a selection of references, see [[Mathematical programming|Mathematical programming]].
 
See also [[Active constraint|Active constraint]]. For a selection of references, see [[Mathematical programming|Mathematical programming]].
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[[Category:Operations research, mathematical programming]]

Latest revision as of 17:58, 14 October 2014

inactive constraint

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 passive (at a solution $y$) if $g_i(y)<0$.

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

How to Cite This Entry:
Passive constraint. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Passive_constraint&oldid=17390
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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