Answers to: Transform non-linear to linear constraints with multiple binary variableshttp://www.or-exchange.com/questions/12270/transform-non-linear-to-linear-constraints-with-multiple-binary-variables<p>Dear OR experts,</p>
<p>I am busy with a complected nonlinear constraint couple of weeks. I have below constraint which is nonlinear and I am trying to find a way to make it linear in order to avoid nonlinear programming.</p>
<p>x=A×(1-(B×Z1)×(C×Z2)×(D×Z3))</p>
<p>where x is a continues variable, Z1, Z2, and Z3 are binary variables, and A, B, C, and D are constant.</p>
<p>I appreciate it if you could help me.</p>
<p>Thanks a lot.</p>enWed, 20 May 2015 03:53:23 -0400Comment by Slavko on Kam's answerhttp://www.or-exchange.com/questions/12270/transform-non-linear-to-linear-constraints-with-multiple-binary-variables#12300<p>This assumption is based on the expression: x=A×(1-(B×Z1)×(C×Z2)×(D×Z3)). Please correct this expression, in order to meet your case.</p>SlavkoWed, 20 May 2015 03:53:23 -0400http://www.or-exchange.com/questions/12270/transform-non-linear-to-linear-constraints-with-multiple-binary-variables#12300Answer by Kamhttp://www.or-exchange.com/questions/12270/transform-non-linear-to-linear-constraints-with-multiple-binary-variables/12298<p>Dear Slavko,</p>
<p>The assumptions are not true in my case.</p>KamTue, 19 May 2015 19:30:19 -0400http://www.or-exchange.com/questions/12270/transform-non-linear-to-linear-constraints-with-multiple-binary-variables/12298Answer by Slavkohttp://www.or-exchange.com/questions/12270/transform-non-linear-to-linear-constraints-with-multiple-binary-variables/12271<p>I assume that the following relationship is true. \[ x = \begin{cases} & A-A\cdot B\cdot C\cdot D \text{ if } z_1=z_2=z_3=1 \\ & A \text{ if } z_1+z_2+z_3 <3 \end{cases} \]</p>
<p>Under this assumption, I can write the following linear conditions, in which \(u\) is binary:
\[
\begin{cases}
& x=A-A\cdot B\cdot C\cdot D\cdot (1-u) \\
& 4\cdot u + z_1+z_2+z_3 \ge 3 \\
& u + z_1+z_2+z_3 \leq 3
\end{cases}
\]</p>SlavkoTue, 19 May 2015 06:41:15 -0400http://www.or-exchange.com/questions/12270/transform-non-linear-to-linear-constraints-with-multiple-binary-variables/12271