Hi everybody,
consider please an optimization problem:
minimize sum S1+S2
Subject to : y - x =< A + S1
x - y =< A + S2
and we want to add two more constraints:
y - x =< B - S3
x - y =< B - S4
where A is a small constant value and B is a large constant value, S1 and S2
are surplus and S3 and S4 are slack variables.
S3 and S4 have to be maximized in objective function. As objective function,
is this correct? :
minimize sum S1+ S2 - S3 -S4
where actually we want to minimize S1 and S2; and maximize S3 and S4.
If it is not correct, what to do ?
Thank you for any guide.
Tobias
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[[alternative HTML version deleted]]
Tobias,
Adding the first constraints yields:
S1 + S2 >= -2A
Similarly adding the second set of constraints:
S3 + S4 <= 2B
If A and B are positive (which you didn't specify) then
The minimum of S1+S2 is -2A, and the maximum of S3+S4 is 2B.
Thus, the minimum of S1+S2-S3-S4 is -2(A+B).
Ravi.
----------------------------------------------------------------------------
-------
Ravi Varadhan, Ph.D.
Assistant Professor, The Center on Aging and Health
Division of Geriatric Medicine and Gerontology
Johns Hopkins University
Ph: (410) 502-2619
Fax: (410) 614-9625
Email: rvaradhan at jhmi.edu
Webpage: http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html
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-----Original Message-----
From: r-help-bounces at stat.math.ethz.ch
[mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Tobias Schlottmann
Sent: Wednesday, July 18, 2007 1:24 PM
To: r-help at stat.math.ethz.ch
Subject: [R] Linear programming question
Hi everybody,
consider please an optimization problem:
minimize sum S1+S2
Subject to : y - x =< A + S1
x - y =< A + S2
and we want to add two more constraints:
y - x =< B - S3
x - y =< B - S4
where A is a small constant value and B is a large constant value, S1 and
S2 are surplus and S3 and S4 are slack variables.
S3 and S4 have to be maximized in objective function. As objective
function, is this correct? :
minimize sum S1+ S2 - S3 -S4
where actually we want to minimize S1 and S2; and maximize S3 and S4.
If it is not correct, what to do ?
Thank you for any guide.
Tobias
---------------------------------
[[alternative HTML version deleted]]
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PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
Hi Tobias, Could you please explain the role of x and y - are they somehow related to S1,S2,S3,S4? Are they constant? Are they additional variable? What was your original problem (without the slack variables)? Regards, Moshe. --- Tobias Schlottmann <tobischlot2002 at yahoo.com> wrote:> Hi everybody, > consider please an optimization problem: > > minimize sum S1+S2 > > Subject to : y - x =< A + S1 > x - y =< A + S2 > > and we want to add two more constraints: > > y - x =< B - S3 > x - y =< B - S4 > > where A is a small constant value and B is a large > constant value, S1 and S2 are surplus and S3 and S4 > are slack variables. > > S3 and S4 have to be maximized in objective > function. As objective function, is this correct? : > > minimize sum S1+ S2 - S3 -S4 > > where actually we want to minimize S1 and S2; and > maximize S3 and S4. > > If it is not correct, what to do ? > > Thank you for any guide. > > Tobias > > > --------------------------------- > > > [[alternative HTML version deleted]] > > ______________________________________________ > R-help at stat.math.ethz.ch mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide > http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, > reproducible code. >