; This problem is to find the minimum distance from a plane to an ellipsoid.
; Mercury takes a long time on this.

MINIMIZE  F
 x^2 + 2 y^2 + 3 z^2 = 20               ; ellipsoid
 3 u + 4 v + 3 w = 54                 ; plane
 F = (x - u)^2 + (y - v)^2 + (z - w)^2      ; square of distance

; exact solution is:  x = 3 , y = 2 , z = 1
;                     u = 6 , v = 6 , w = 4
;                     F = 34

{ starting values }
 x := 0
 y := 0
 z := 0
 u := 8
 v := 8
 w := 8

 DIGITS 6
 PROGRESS x