cast multiplication of floats to integer

Answered

Saeid Ghafouri

March 20, 2023 22:46

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Is there a way to cast a multiplication (of two floating points) result to integer inside a gurobi constraint definition?

Related to

• Python

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  Jaromił Najman

  • Gurobi Staff

  March 21, 2023 10:12 Edited

  Hi Saeid,

  Do you mean to introduce a rounding constraint, e.g., something like \(i = \lfloor x\cdot y \rfloor\), where \(i\) is integer and \(x,y\) are continuous variables?

  This can be achieved by the inequality constraints

  \[\begin{align*}
  i \leq x\cdot y \leq i +1
  \end{align*}\]

  These inequalities would force \(i\) to the rounded down value of \(x\cdot y\). Note that there is a special case when \(x\cdot y\) are indeed integer, e.g., \(=2\). Then the value of \(i\) is not fixed and could be \(1\) or \(2\). To avoid such cases, one could introduce a small constant tolerance \(\epsilon > 0\) and apply it to one of the inequalities.

  Best regards, 
  Jaromił

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