Active-set method: Difference between revisions

Revision as of 09:07, 13 December 2011

Revision as of 21:51, 22 December 2011

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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 hyperplanes that intersect at the solution point. In [[quadratic programming]], as the solution is not mandatorilynecessarily 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.

In general an active set algorithm has the following structure: