From: Walter Roberson on
Kiril wrote:
>> You can see trivially that a maximum does not exist: since x2 appears
>> linearly, for any given x1, one of x2 = infinity or x2 = -infinity
>> will be infinity.
>
> O.K. ... but i have to write code to prove it! that's my project!

Any such algorithm should start by testing each combination of variables
at +/- infinity together with one intermediate point (such as 0) to see
whether the function is indeed constrained output. Those preliminary
tests to verify that a maximizer will work, would show that the function
has no maximum.
From: Kiril on
Tnaks ... I do it!