
Re: An optimization problem
Posted:
Sep 7, 2013 6:21 PM


On Saturday, September 7, 2013 12:49:51 PM UTC7, quasi wrote: > analyst41 wrote: > > > > >consider f(x1,x2,...xn) = {1 + sum(xi)^2)} / {1 +sum{x(i)} > > > > > >0 <=xi <=1 for all i. > > > > > >The maximum function value of 1 occurs at either > > >all x's = 0 or all x's = 1. > > > > > >Can an explicit formula be given for the minimum? > > > > Yes. > > > > The minimum value is > > > > ((2n)*((n+1)sqrt(n^2+n)))/sqrt(n^2+n) > > > > which occurs when all x's are equal to > > > > (sqrt(n^2+n)  n)/n > > > > quasi
This formula is incorrect: it should be (as in my previous post) all x = [sqrt(n+1)1]/n. This can be verified numerically using an optimization package such as LINGO or the Maple Optimization facility or the EXCEL Solver, etc.

