The min(x,y) constraint is also a linear constraint, and can be coded using
binary variables.
obj: min x
s.t. x + y >= 8
z1 = ....
z2 < ....
-1*(1-s1)M <= y - z1 <= 0
-1*(1-s2)M <= y - z2 <= 0
s1 + s2 = 1
s1, s2 \in {0,1}
This formulation will lock y to the minimum of z1 and z2. M is a huge +ve
constant in this.
Disadvantages of the above formulation:
1. s1,s2 are binary and hence this formulation could potentially be slower.
2. sometimes, the constant M can affect the tolerance / robustness of the
solution. You can read more literature to learn how and why.
I would also suggest that you read about disjunctive programming which
teaches how to encode if-else type of constraints in linear forms.
Hopefully it helps.
Manish Jain
University of Southern California
On Tue, Jul 20, 2010 at 2:36 PM, xiaomi <[email protected]> wrote:
> No. Not their sum. For example this problem:
>
> Object: minimize X
> Constraint: X+Y>=8, Y=min(Z1,Z2) Z1=...., Z2<.....
>
> Do I describe Y as "Y<=Z1, Y<=Z2" ? That is not correct unless I maxmize Y
> in my object at the same time as minimizing X. So I asked whether multiple
> objects are functional.
>
>
>
>
>
> Mansour Moufid :
>
> 2010/7/20 xiaomi <[email protected]>:
>>
>>
>>> I am running a project that need to minimize more than one variable in
>>> LP solver. Can GLPK do that? If yes, how to do so?
>>>
>>>
>>
>> Minimize their sum?
>>
>>
>>
>
>
> _______________________________________________
> Help-glpk mailing list
> [email protected]
> http://lists.gnu.org/mailman/listinfo/help-glpk
>
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