Complementary slackness

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The condition that two non-negative vectors are orthogonal. It arises in the Kuhn-Tucker conditions, where the Lagrange multiplier, say LaTeX: y, must be orthogonal to the (inequality) constraint functional value: LaTeX: y^T g(x)=0. This means either LaTeX: y_i=0 or LaTeX: g_i(x)=0 for each LaTeX: i -- that is, if a constraint is not active, its Lagrange multiplier must be zero.


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