***K***arush-***K***uhn-***T***ucker (KKT) Conditions - Used to find optimal solution of a general nonlinear programming (NLP) problem - Requires $f(x)$ to be concave and differentiable, $g_i(x)$ to be convex 1. $\frac{\partial f}{\partial x_j} - \sum_{i=1}^m u_i\frac{\partial g}{\partial x_j} \leq 0$ 2. $x_j\bigg(\frac{\partial f}{\partial x_j} - \sum_{i=1}^m u_i\frac{\partial g}{\partial x_j}\bigg) = 0$ 3. $g_i(\textbf{x})-b_i \leq 0$ 4. $u_i[g_i(\textbf{x})-b_i] \leq 0$ 5. $x_j \geq 0$ 6. $u_i \geq 0$ - $i$ - index of constraints - $j$ - index of decision variables - $m$ - number of constraints - $n$ - number of decision variables