I want to minimize an object function $f(x,y,z,t)$ e.g.

f = 1/2 a^2 E^(-2 d^2 t) (E^(2 a x)+E^(2 a y)+E^(2 a z)+2 E^(a (y+z)) Cos[d x+a z] Sin[a x+d y]+2 E^(a (x+y)) Cos[a y+d z] Sin[d x+a z]+2 E^(a (x+z)) Cos[a x+d y] Sin[a y+d z])

with respect to $a$ and $d$ and for all $t, theta$ and $z$ under the conditions: $t \ge 0$, $x=r\cos[\theta]$, $y=r\sin[\theta]$, $0 < \theta \le 2\pi$ and $0 < z \le m$ and $0 < r \le R$. I first replaced all $x$ and $y$, then applied Minimize with the constraints:

Minimize[{f /. {x->r*Cos[theta],y->r*Sin[theta]}, 0 < theta <= 2*Pi && 0 < z <= m && 0 < r <= R && t >= 0}, {a,d}]

Mathematica simply returns the same input to me. I also tried NMinimize but no luck. How can I fix this please?