An inequality constraint is active when $h^{(j)} (x) = 0$. This means that the optimum might change were that constraint removed.

Michigan State University

Describe $\mathbb{S}$ with $m$ functions $g^{(i)}$ and $n$ functions $h^{(j)}$ s.t. $\mathbb{S}=\{x | \forall i, g^{(i)} (x) = 0$ and $\forall j, h^{(j)} (x) \le 0 \}$.

Equations with $g^{(i)}$ are equality constraints. Equations with $h^{(j)}$ are inequality constraints

KKT Step 1: Equality and Inequality Constraints

Goodfellow, I., Bengio, Y., & Courville, A. (2016). $\mathit{Deep \ Learning.}$ MIT Press. Retrieved from [www.deeplearningbook.org](https://www.deeplearningbook.org) 

Learn Before

Related