- Have function of two variables $f(x_1, x_2)$
- can separate into functions of one variable $f(x_1)+f(x_2)$
- Assumptions
- obj. function is concave
- constraint functions are convex
- all functions are separable
- Two cases:
1. Piecewise linear function of single variable
![[case1.png]]
2. Approximate nonlinear function as piecewise linear function
![[case2.png]]
## Non-concave Objective Function
Slopes increase as $x_j$ increases
$
\begin{align}
x_{j2} = 0 \quad &\text{when} \quad x_{j1} < u_{j1} \\
x_{j3} = 0 \quad &\text{when} \quad x_{j2} < u_{j2}
\end{align}
$
Introduce binary variables:
$
\begin{align}
q_1 =
\begin{cases}
\end{cases}
\end{align}
$