linearize the a*b equation

GAMS
1

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.

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2

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






On Tue, May 29, 2012 at 4:06 PM, Fatemi wrote:

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.

–
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3

I want to linearize the following equation in the format of MILP:
D=abc;
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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4

You can use McCormick linearization.
OF=e=x1-x2-y1-x1y1
OF=e=x1-x2-y1-w1
x1y1
w1_mc1… x1Ly1+y1Lx1-x1Ly1L-w1=l=0;
w1_mc2… x1Uy1+y1Ux1-x1Uy1U-w1=l=0;
w1_mc3… -x1Uy1-y1Lx1+x1Uy1L+w1=l=0;
w1_mc4… -x1Ly1-y1Ux1+x1L*y1U+w1=l=0;
x1L=x1lower
x2U=x2 upper

2012/5/29 Fatemi

I want to linearize the following equation in the format of MILP:
D=abc;
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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5

Thanks a lot. But I cannot relate my function (D=abc) 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

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6

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


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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: adrud@arki.dk



From: gamsworld@googlegroups.com [mailto:gamsworld@googlegroups.com] On Behalf Of Fatemi
Sent: Tuesday, May 29, 2012 1:12 PM
To: gamsworld@googlegroups.com
Subject: Re: linearize the ab equation



I want to linearize the following equation in the format of MILP:
D=ab*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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7

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

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