I have the following problem, when I am trying to optimize function with pre-defined assumptions.
I am using Mathematica 8 and I wrote the following simple code
$Assumptions = (m > 0)
Minimize[{x^m, x >= 1}, x]
It is clear, that the answer is 1, since $x^m\ge 1$ if $x\ge 1$ for all positive $m$. However, Mathematica fails to calculate this simple problem.
What do I do wrong? Should I use another function for minimization?
$Assumtpionswill only be used by functions which themselves have anAssumptionsoption. I know this doesn't solve your problem, but at least it clarifies why this doesn't work. It seems sometimes it's possible to include assumptions on the parameters in the constraint list, but in this case it doesn't work. – Szabolcs Jun 6 '12 at 12:40mminimize x^m when x >= 1 and m>=0andminimize x^m when x >= 1 and m<0in Wolfram Alpha! The first question is bestowed with a better fitting answer than the second one. As for $0>m>-\infty$ the function $x^m$ has no global minimum the second answer suffers from numerical defects. – PlatoManiac Jun 6 '12 at 13:35Minimize[{x^m,x>=1&&m>0},x](additional condition explicitly given) andMinimize[{x^(Abs[m]+1/10),x>=1},x](the exponent being obviously positive).Minimize[{x^2,x>=1},x]works fine, however. – celtschk Jun 6 '12 at 19:10