quasi
Posts:
12,018
Registered:
7/15/05


Re: An optimization problem
Posted:
Sep 8, 2013 3:36 AM


William Elliot wrote: >analyst41@hotmail.com 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? > >Let g(x) = (1 + x^2)/(1 + x) and look for extreme values of g.
The function g is not applicable.
From the context, the OP intended
f(x_1, ..., x_n) = (1 + sum((x_i)^2))/(1 + sum(x_i))
whereas you interpreted it (incorrectly) as
f(x_1, ..., x_n) = (1 + (sum(x_i))^2))/(1 + sum(x_i))
Of the two possible interpretations above, only the first is consistent with the OP's claim that for all n, the maximum value of f is 1.
quasi

