RE: [Help-glpk] The "dual" suffix and sensitivity to how a constraint is expressed in GMPL

[Meketon, Marc]

Xypron,

I thank you for your very speedy reply.  And I appreciate your explanation - 
it's very clear.  I do wonder if a special case should be made when only one 
side has variables.  I have somewhat mixed feelings about that - special cases 
in general are confusing, but superfluous sign reversals are confusing as well.

Indeed, I did change the constraints to put all the constants on the right-hand 
side.

Maybe your update of the wiki should go a little further and give a clearer 
explanation.  In addition to saying:

"The duals will be calculated based on the standard form of the constraints."

Maybe your should add on the sentences:

For example, the GMPL constraint "1 = c * y" will be transformed into "-c * y = 
-1", and the dual value generated will be the negative of the value if the 
constraint was written as "c * y = 1".  Generally, it is good idea to put the 
constant term on the right-hand-side when obtaining duals are important for 
subsequent non-GLPK related calculations.

-Marc

-----Original Message-----
From: glpk xypron [mailto:address@hidden
Sent: Tuesday, December 28, 2010 5:00 PM
To: Meketon, Marc; address@hidden
Subject: Re: [Help-glpk] The "dual" suffix and sensitivity to how a constraint 
is expressed in GMPL

Hello Marc,

in the general case a constraint may have the form:

a + sum b[i] x[i] <=> c + sum d[i] x[i];

Now all columns have to be moved to the left and all constants to the right 
giving you:

sum (b[i]-d[i]) x[i] <=> c - a;

Giving your special case a special treatment might create results that are not 
intuitive in a different context.

Why do you not always write the columns on the left hand side and the constants 
on the right hand side?

The code in question is in glpk-4.45/src/glpmpl03.c, function take_member_con, 
where you can find the transformation rules:
/* constraint a * x + b >= c * y + d is transformed to the
   standard form a * x - c * y >= d - b */
/* constraint a * x + b <= c * y + d is transformed to the
   standard form a * x - c * y <= d - b */
/* constraint a * x + b = c * y + d is transformed to the
   standard form a * x - c * y = d - b */
/* ranged constraint c <= a * x + b <= d is transformed to
   the standard form c - b <= a * x <= d - b */

I have updated
http://en.wikibooks.org/wiki/GLPK/Steps_of_GMPL_File_Processing#Model_generation

Best regards

Xypron


-------- Original-Nachricht --------
> Datum: Tue, 28 Dec 2010 15:22:19 -0600
> Betreff: [Help-glpk] The "dual" suffix and sensitivity to how a
> constraint is expressed in GMPL

> I came across a curious quirk in the use of the new suffixes in GMPL:
> how a constraint is formed leads to non-intuitive dual results.
>
> This model:
>   # Simple Model 1
>   var x1 >= 0;
>   var x2 >= 0;
>   var s1 >= 0;
>   var s2 >= 0;
>
>   s.t. constraint1 : 1.0 = 0.1*x1 + x2 + s1;
>   s.t. constraint2 : 1.0 = x1 + 0.2*x2 + s2;
>   minimize obj: -x1 - x2;
>
>   solve;
>
>   display constraint1.dual;
>   display constraint2.dual;
>
>   end;
>
> displays the two duals as
>   constraint1.dual = 0.816326530612245
>   constraint2.dual = 0.918367346938776
>
> But changing how constraint1 and constraint2 are written to:
>   s.t. constraint1 : 0.1*x1 + x2 + s1 = 1.0;
>   s.t. constraint2 : x1 + 0.2*x2 + s2 = 1.0; displays the two duals as
>   constraint1.dual = -0.816326530612245
>   constraint2.dual = -0.918367346938776
>
> Using the "--wlp" option, it's easy to see what is occuring.  In the
> first case, the "wlp" output is:
>   \* Problem: simple *\
>
>   Minimize
>    obj: - x1 - x2
>
>   Subject To
>    constraint1: - 0.1 x1 - x2 - s1 = -1
>    constraint2: - x1 - 0.2 x2 - s2 = -1
>
>   End
> and in the second case the "wlp" output is:
>
>   \* Problem: simple *\
>
>   Minimize
>    obj: - x1 - x2
>
>   Subject To
>    constraint1: + 0.1 x1 + x2 + s1 = 1
>    constraint2: + x1 + 0.2 x2 + s2 = 1
>
>   End
> By switching around the terms on the "=" sign, GMPL reversed the signs
> of all of the coefficients.  Which reversed the signs on the duals.
>
> I'm not a fan of the changing of the sign when I plan to use the duals
> for calculations later on; it leads to somewhat random behavior, and
> makes using the new suffixes a little scary for bigger models when it
> is not easy to know the correct sign for each constraint.  Is there
> really a need to change the signs?  I would hope this could be turned off.
>
> -Marc
>
>
>
>
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