# Complementary slackness

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.