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
Kam |

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
Slavko |