[Help-glpk] Piecewise Linear Function

[Simone Atzeni]

Hi,


I have a piecewise linear function like this:




\[ 

h_i({\bf x},{\bf u})= 

\begin{cases} 

A_1({\bf x}) + {\bf u} (B_1({\bf x}) - A_1({\bf x})),   \text{se $0 \le {\bf u} 
< 1$} \\ 

B_1({\bf x}) + ({\bf u}-1) (B_2({\bf x}) - B_1({\bf x})),   \text{se $1 \le 
{\bf u} < 2$} \\ 

B_2({\bf x}) + ({\bf u}-2) (B_3({\bf x}) - B_2({\bf x})),   \text{se ${\bf u} 
\ge 2$} \\ 

\end{cases} 

\] 




where:




\begin{itemize} 

\item $A_1({\bf x}) = 3x$

\item $B_1({\bf x}) = 4x$

\item $B_2({\bf x}) = 5x$

\item $B_3({\bf x}) = 6x$

\end{itemize} 




This function represents the constraints in a MILP.




To solve this MILP I have to convex my function, but I don't know like do it.




Somebody can help me?




Thanks

Simone

Hi,

I have a piecewise linear function like this:

\[ 

h_i({\bf x},{\bf u})= 

\begin{cases} 

A_1({\bf x}) + {\bf u} (B_1({\bf x}) - A_1({\bf x})), & \text{se $0 \le {\bf u} < 1$} \\ 

B_1({\bf x}) + ({\bf u}-1) (B_2({\bf x}) - B_1({\bf x})), & \text{se $1 \le {\bf u} < 2$} \\ 

B_2({\bf x}) + ({\bf u}-2) (B_3({\bf x}) - B_2({\bf x})), & \text{se ${\bf u} \ge 2$} \\ 

\end{cases} 

\] 

where:

\begin{itemize} 

\item $A_1({\bf x}) = 3x$

\item $B_1({\bf x}) = 4x$

\item $B_2({\bf x}) = 5x$

\item $B_3({\bf x}) = 6x$

\end{itemize} 

This function represents the constraints in a MILP.

To solve this MILP I have to convex my function, but I don't know like do it.

Somebody can help me?

Thanks

Simone