I have a multivariate function that I seek to maximize (ideally symbolically):
The function has the form:
$\frac{(-j*a)}{8 (-(b/2) - j (c-d-e)) ((j*b*c)/2 - (j*b*d)/2 + c*d - d^2 + a^2/4))}$
(where j is the imaginary number) I want to find the maximums of the real and imaginary parts. When I try to find them with the code:
Maximize[Im[function], {a, b, c, d, e}]
It tells me that my solution is indeterminate and that my maximum is at infinity. I believe that this issue is due to the function "blowing up" if all the values in the denominator are zero. So I wanted to write a code that ignores these cases when the parameters are zero.
I did this by adding
Maximize[Im[function], a>0, b>0, c>0,d>0, e>0, {a, b, c, d, e}]
In doing so, Mathematica "hangs" and I never get an answer.
Any ideas or suggestions for how I should proceed? Should I give up on finding a symbolic solution and go straight to using a numerical solver? It seems like a simple enough function that finding a maximum doesn't /seem/ impossible but maybe my intuition is wrong..
The code that hangs is:
fun = -((I a)/(
8 (-(b/2) - I (c - d - e)) ((I b c)/2 - (I b d)/2 + c d - d^2 +
a^2/4)));
imFUN = ComplexExpand[Im[fun]] // Simplify
Maximize[imFUN ,
a > 0 && b > 0 && c > 0 && d > 0 && e > 0, {a, b, c, d, e}]