I'm modeling an LP problem in which I have to maximize an objective function. Two of the constraints are the following, where $k_i$ are constants and $x_i$ decision variables (continuous). Could anyone help me on how to linearize these constraints? \begin{align} \text{max}{[(x_1 + k_1), (x_2 + x_3 + x_4)]} &\leq k_2\\ \text{min}{[(x_1 + k_1), (x_2 + x_3 + x_4)]} &\geq -k_2 \end{align}
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$\max(y,z)\le b$ is equivalent to \begin{align} y&\le b\\ z&\le b \end{align} The $\min$ constraint is similar.
