
From:  Simone Atzeni 
Subject:  [Helpglpk] Piecewise Linear Function 
Date:  Fri, 27 Feb 2009 15:41:31 +0300 
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 
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