linearize the a*b equation

[Fatemi]

Dear readers,

I want to linearize the following equatuion in the format of MILP:
c=a*b;
where 'a' and 'b' are continous variable and also 0<a<1; 0<=b<=1.

Thanks in advance.

[Mohammad Reza Abbasi]

Dear

Are you sure that it is possible to transform a continuous variable into an integer one? May I know what is your model is all about?

Best Regards,

Mohammad Reza Abbasi, AMIChemE
Postgraduate student (M. Eng.)
Process Systems Engineering Centre
Faculty of Chemical Engineering

Universiti Teknologi Malaysia (UTM)
81310 Skudai, Johor, Malaysia

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[Fatemi]

I want to linearize the following equation in the format of MILP:
D=a*b*c;
where 'a' and 'b' are continuous variables with 0<a<1; 0<=b<=1. 'c' is binary variable.

Thanks in advance.

[olcay emin]

 You can use McCormick linearization.
OF=e=x1-x2-y1-x1*y1

OF=e=x1-x2-y1-w1

*x1*y1
w1_mc1.. x1L*y1+y1L*x1-x1L*y1L-w1=l=0;
w1_mc2.. x1U*y1+y1U*x1-x1U*y1U-w1=l=0;
w1_mc3.. -x1U*y1-y1L*x1+x1U*y1L+w1=l=0;
w1_mc4.. -x1L*y1-y1U*x1+x1L*y1U+w1=l=0;

x1L=x1lower

x2U=x2 upper

2012/5/29 Fatemi <yazdan...@gmail.com>

I want to linearize the following equation in the format of MILP:
D=a*b*c;
where 'a' and 'b' are continuous variables with 0<a<1; 0<=b<=1. 'c' is binary variable.

Thanks in advance. --

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[Fatemi]

 

Thanks a lot. But I cannot relate my function (D=a*b*c) with your function.I would appreciate if you made it clear for me.

In other words, how can I use your suggested equation in order to liberalize my function?

Regards

[Arne Stolbjerg Drud]

Fatima:

 

You expression is nonlinear and it cannot be linearized. One of the answers gave you lower and upper bounds on D as functions of a, b, and c, and their bounds this is a good as it gets. For the particular bounds you have on your variables the tightest possible linear inequalities on D become:

 

D =G= 0; (not needed for a positive variable)

D =L= a;

D =L= b;

D =L= c;

 

If you cannot live with an approximation you must use an MINLP solver instead, in which case you can use your nonlinear equation directly.

 

Regards

 

Arne

 

-------------------------------------------

Arne Stolbjerg Drud

ARKI Consulting & Development A/S

Bagsvaerdvej 246A, DK-2880 Bagsvaerd, Denmark

Phone: (+45) 44 49 03 23, Fax: (+45) 44 49 03 33, email: ad...@arki.dk

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[Fatemi]

thanks a lot Arne.
but can you help me with McCormick linearization?