On 10/17/07, Ravi Varadhan <[EMAIL PROTECTED]> wrote: > What if simultaneously maximizing f(x,y) and g(x,y) is an incompatible > objective? > > Modifying Duncan's example slightly, What if: > > f(x,y) = -(x-y)^2 and > g(x,y) = -(x-2)^2-(y-x-1)^2? > > Here: > (1) => x = y > (2) => y = x + 1 > (3) => x = y => no solution! > > In order for a solution to necessarily exist, one needs to define a scalar > function that strikes a compromise between f and g.
But imagine that one is sure that there is no incompatibility, how can R get the solution? For instance, can R get the solution for Duncan's example? Paul > > 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 Alberto Monteiro > Sent: Wednesday, October 17, 2007 2:30 PM > To: Duncan Murdoch; Paul Smith > Cc: r-help > Subject: Re: [R] Multi-objective optimization > > Duncan Murdoch wrote: > > > >> Is there any package to do multi-objective optimization? For instance, > >> consider the following problem: > >> > >> maximize f(x,y) in order to x > >> > >> and > >> > >> maximize g(x,y) in order to y, > >> > >> simultaneously, with x and y being the same both for f and g. Can R do > >> it numerically? > > > > I don't think the problem is well posed. For example, what's the > > solution if f(x,y) = -(x-y)^2 and g(x,y) = -(x-2)^2-(y-1)^2? The > > first is maximized at x=y, the second at x=2, y=1, so in order to > > choose a solution you need to specify what sort of tradeoff to use > > to combine the two objectives. > > > I guess the problem was not well _defined_. > > I "interpreted" it as: > > maximize f(x,y) in order to x %means% > (1) for every y, find x = f1(y) such that f(x,y) is max > > maximize g(x,y) in order to y %means% > (2) for every x, find y = g1(x) such that g(x,y) is max > > simultaneously %means% > (3) x = f1(y) and y = g1(x). > > So, for your example, we would have: > (1) => x = y > (2) => y = 1 > (3) => x = y = 1 > > Alberto Monteiro > > ______________________________________________ > R-help@r-project.org 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@r-project.org 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.
