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The first sentence must inform the lay reader that mathematics is what this is about. "In optimization" doesn't do that. |
Linked "hyperplanes" to the wiki page for itself. |
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is called '''active''' at <math>x</math> if <math>g_i(x)=0</math> and '''inactive''' at <math>x</math> if <math>g_i(x)>0.</math> Equality constraints are always active. The '''active set''' at <math>x</math> is made up of those constraints <math>g_i(x)</math> that are active at the current point {{harv|Nocedal|Wright|2006|p=308}}.
The active set is particularly important in optimization theory as it determines which constraints will influence the final result of optimization. For example, in solving the [[linear programming]] problem, the active set gives the [[Hyperplane|hyperplanes]] that intersect at the solution point. In [[quadratic programming]], as the solution is not necessarily on one of the edges of the bounding polygon, an estimation of the active set gives us a subset of inequalities to watch while searching the solution, which reduces the complexity of the search.
==Active set methods==
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