Transform non-linear to linear constraints with multiple binary variables

 0 Dear OR experts, 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. x=A×(1-(B×Z1)×(C×Z2)×(D×Z3)) where x is a continues variable, Z1, Z2, and Z3 are binary variables, and A, B, C, and D are constant. I appreciate it if you could help me. Thanks a lot. asked 19 May '15, 03:32 Kam 21●2●9 accept rate: 0%

 1 I assume that the following relationship is true. $x = \begin{cases} & A-A\cdot B\cdot C\cdot D \text{ if } z_1=z_2=z_3=1 \\ & A \text{ if } z_1+z_2+z_3 <3 \end{cases}$ Under this assumption, I can write the following linear conditions, in which $$u$$ is binary: $\begin{cases} & x=A-A\cdot B\cdot C\cdot D\cdot (1-u) \\ & 4\cdot u + z_1+z_2+z_3 \ge 3 \\ & u + z_1+z_2+z_3 \leq 3 \end{cases}$ answered 19 May '15, 06:41 Slavko 205●1●5 accept rate: 12%
 0 Dear Slavko, The assumptions are not true in my case. answered 19 May '15, 19:30 Kam 21●2●9 accept rate: 0% 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. (20 May '15, 03:53) Slavko
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