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.


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's gravatar image

accept rate: 0%

edited 19 May '15, 03:51

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's gravatar image

accept rate: 12%

edited 19 May '15, 13:09

Dear Slavko,

The assumptions are not true in my case.


answered 19 May '15, 19:30

Kam's gravatar image

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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Asked: 19 May '15, 03:32

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Last updated: 20 May '15, 03:53

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