Could someone help me to solve the following problem?
A class of piecewise linear functions can be represented as $f(x) = Maximum (c_{1}^Tx+ d_{1}, c_{2}^Tx, \cdots, c_{p}^Tx + d_{p})$. For such a function $f$, consider the problem \begin{equation*} \text{minimize} \hspace{.8em} f(x)\\ \text{subject to} \hspace{.8em} Ax = b\\ \hspace{2 cm} x \geq 0. \end{equation*} Show how to convert this problem to a linear programming problem.
Regards,
R3
Introduce a new variable $y$, and rewrite as follows: \begin{array}{ll} \text{minimize} & y \\ \text{subject to} & c_i^Tx + d_i \leq y, ~i=1,2,\dots, p \\ &A x = b \\ &x \geq 0 \end{array}