quasi
Posts:
12,021
Registered:
7/15/05


Re: An optimization problem
Posted:
Sep 8, 2013 2:04 AM


Ray Vickson wrote: >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.
Yes, agreed.
I used Maple for the algebra, but didn't notice that I had a typo in my input.
quasi

