[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]] __ R-help@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.
Re: [R] Linear programming question
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: [EMAIL PROTECTED] Webpage: http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html -Original Message- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Tobias Schlottmann Sent: Wednesday, July 18, 2007 1:24 PM To: r-help@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]] __ R-help@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. __ R-help@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.
Re: [R] Linear programming question
Tobias, Just a clarification/correction to my solution: it makes no difference whether A and B are positive or negative. The minimum of S1+S2-S3-S4 is always -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: [EMAIL PROTECTED] Webpage: http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html -Original Message- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Ravi Varadhan Sent: Wednesday, July 18, 2007 1:52 PM To: 'Tobias Schlottmann'; r-help@stat.math.ethz.ch Subject: Re: [R] Linear programming question 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: [EMAIL PROTECTED] Webpage: http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html -Original Message- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Tobias Schlottmann Sent: Wednesday, July 18, 2007 1:24 PM To: r-help@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]] __ R-help@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. __ R-help@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. __ R-help@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.
Re: [R] Linear programming question
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 [EMAIL PROTECTED] 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@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. __ R-help@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.
