# Finding minimum for a function of four variables [closed]

I would like to find the min of the following function,

-5 + 2 Sqrt[5] + 4 (5 - 3 Sqrt[5]) b^2 + Sqrt[2] (-1 + 2 b^2 - 2 a Sqrt[1 - a^2 -
2 b^2] Cos[ρ - ϛ])


for -1 ⩽ a ⩽ 1 -((1 - a^2)/2)^(1/2) ⩽ b ⩽ ((1 - a^2)/2)^(1/2) 0 ⩽ ρ ⩽ 2*Pi 0 ⩽ ϛ ⩽ 2*Pi

• Seems like the sort of thing one finds in the documentation. Feb 9, 2020 at 13:18

f = -5 + 2 Sqrt[5] + 4 (5 - 3 Sqrt[5]) b^2 + Sqrt[2] (-1 + 2 b^2 -

{5 - 4 Sqrt[5], {a -> 0, b -> -(1/Sqrt[2]), ρ -> 27/22, ϛ -> 1/22 (27 + 11 π)}}