Math — KKT Conditions
Optimality with inequality constraints.
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\nabla f = \sum_i \mu_i \nabla g_i
\mu_i\, g_i(x) = 0 \;\text{(complementary slackness)}
\mu_i \geq 0
g_i(x) \leq 0
Optimality with inequality constraints.
\nabla f = \sum_i \mu_i \nabla g_i
\mu_i\, g_i(x) = 0 \;\text{(complementary slackness)}
\mu_i \geq 0
g_i(x) \leq 0