How to add a constraint that involves multiplication?

[Muhammad Bilal]

Hi All,

Can someone instructs me about specifying a constraint in Gurobi Java API that involves multiplication, like the one given below (for Matlab version):

a.*const >= 0; where a is the array of decision variable values while const is the constant.

I can't see any method in GRBLinExpr to specify this kind of constraint. Is this a quadric constraint?

Your guidance will be highly appreciated.

Thanks in advance

Kind Regards

Bilal

[Renan Garcia]

  a.*const >= 0

is equivalent to

  a(1) * const >= 0

  a(2) * const >= 0

  ...

If const > 0, then that is equivalent to

  a(1) >= 0

  a(2) >= 0

  ...

and you can enforce this without a constraint by setting the LB attribute (http://www.gurobi.com/documentation/6.5/refman/lb.html#attr:LB) for each variable in a to 0. Fortunately, this is the default for Gurobi unless otherwise specified.

If const < 0, then that is equivalent to

  a(1) <= 0

  a(2) <= 0

  ...

and you'll need to set the LB attribute to -GRB.INFINITY (if necessary) and UB attribute to 0 (GRB.INFINITY by default).

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[Muhammad Bilal]

Hi Renan Garcia,

Many thanks for the clarification and very nice explanation. I got it right now.

Kind Regards,

Bilal

[Muhammad Bilal]

In my case, always const > 0 holds, which means the first case you mentioned. Since Gurobi API by default take care by this, which mean this constraint can be skipped, without compromising the results of the model.

Am I right?

On Thursday, July 14, 2016 at 3:08:22 PM UTC+1, Renan Garcia wrote:

[Renan Garcia]

Yes

[Muhammad Bilal]

I appreciate your help.

Thanks a lot.