Active-set method: Difference between revisions

Revision as of 16:13, 4 June 2013

Revision as of 20:33, 4 August 2013

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:<math>g_1(x)\ge 0, \dots, g_k(x)\ge 0</math>

that define the ''[[feasible region'']], that is, the set of all ''x'' to search for the optimal solution. Given a point <math>x</math> in the feasible region, a constraint

:<math>g_i(x) \ge 0</math>

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}}.