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## Re: [Help-glpk] Can GLPK use multiple object?

 From: Manish Jain Subject: Re: [Help-glpk] Can GLPK use multiple object? Date: Tue, 20 Jul 2010 14:46:01 -0700

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.

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 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 :

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?

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