tp109v2.apm

```Model tp109v2
! Source version 1

! See also tp109v1.
! tp109v2 is the same as tp109v1 except that each
! equality constraint has been replaced by two inequalities.
! FMC version 8.1 has problems with tp109v1.

Parameters
c22938a = -22.938 ! from PROB.FOR
c22938b =  22.938 ! from H+S, seems to be a typo
c22938  = c22938a ! my quite clear decision from data below
a = 50.176
arg = 0.25
b = sin(arg)
c = cos(arg)
End Parameters

Variables
x[1] = 0, >=    0
x[2] = 0, >=    0
x[3] = 0, >=   -0.55, <=   0.55
x[4] = 0, >=   -0.55, <=   0.55
x[5] = 0, >=  196,    <= 252
x[6] = 0, >=  196,    <= 252
x[7] = 0, >=  196,    <= 252
x[8] = 0, >= -400,    <= 800
x[9] = 0, >= -400,    <= 800
obj
End Variables

Intermediates
cf[ 1] = x[4] - x[3] + .55
cf[ 2] = x[3] - x[4] + .55
cf[ 3] = 2250000 - x[1]^2 - x[8]^2
cf[ 4] = 2250000 - x[2]^2 - x[9]^2
cf[ 5] = x[5]*x[6]*sin((-1)*x[3] - 1/4)   &
+ x[5]*x[7]*sin((-1)*x[4] - 1/4)   &
+ 2*b*x[5]^2 - a*x[1] + 400*a
cf[ 6] = x[5]*x[6]*sin(x[3] - 1/4)        &
+ x[6]*x[7]*sin(x[3] - x[4] - 1/4) &
+ 2*b*x[6]^2 - a*x[2] + 400*a
cf[ 7] = x[5]*x[7]*sin(x[4] - 1/4)        &
+ x[6]*x[7]*sin(x[4] - x[3] - 1/4) &
+ 2*b*x[7]^2 + 881.779*a
cf[ 8] = a*x[8]                           &
+ x[5]*x[6]*cos((-1)*x[3] - 1/4)   &
+ x[5]*x[7]*cos((-1)*x[4] - 1/4)   &
- 200*a - 2*c*x[5]^2               &
+ 0.7533e-3*a*x[5]^2
cf[ 9] = a*x[9]                           &
+ x[5]*x[6]*cos(x[3] - 1/4)        &
+ x[6]*x[7]*cos(x[3] - x[4] - 1/4) &
- 2*c*x[6]^2 + 0.7533e-3*a*x[6]^2  &
- 200*a
cf[10] = x[5]*x[7]*cos(x[4] - 1/4)        &
+ x[6]*x[7]*cos(x[4] - x[3] - 1/4) &
- 2*c*x[7]^2 + c22938*a            &
+ 0.7533e-3*a*x[7]^2
mf     = 3*x[1] + 1.0e-6*x[1]^3 + 2*x[2]  &
+ 0.522074e-6*x[2]^3
End Intermediates

Equations
cf[1: 4] >= 0
cf[5:10] >= 0
-cf[5:10] >= 0

obj = mf

! best known objective = 5362.069181109596
! begin of best known solution
! x[1] =  675.0253392597418
! x[2] = 1134.021089714841
! x[3] =    0.1334850509182756
! x[4] =   -0.37119026264778
! x[5] =  252
! x[6] =  252
! x[7] =  201.4658577338128
! x[8] =  426.6190056621182
! x[9] =  368.4881990875219
! end of best known solution

! c22938 = c22938a ! best known objective = 5362.069181109596
! c22938 = c22938a ! begin of best known solution
! c22938 = c22938a ! x[1] =  675.0253392597418
! c22938 = c22938a ! x[2] = 1134.021089714841
! c22938 = c22938a ! x[3] =    0.1334850509182756
! c22938 = c22938a ! x[4] =   -0.37119026264778
! c22938 = c22938a ! x[5] =  252
! c22938 = c22938a ! x[6] =  252
! c22938 = c22938a ! x[7] =  201.4658577338128
! c22938 = c22938a ! x[8] =  426.6190056621182
! c22938 = c22938a ! x[9] =  368.4881990875219
! c22938 = c22938a ! end of best known solution

! c22938 = c22938b ! best known objective = 5326.851330086209
! c22938 = c22938b ! begin of best known solution
! c22938 = c22938b ! x[1] =  669.1097610257111
! c22938 = c22938b ! x[2] = 1131.663146223707
! c22938 = c22938b ! x[3] =    0.1329592125985436
! c22938 = c22938b ! x[4] =   -0.3604243084232723
! c22938 = c22938b ! x[5] =  252
! c22938 = c22938b ! x[6] =  252
! c22938 = c22938b ! x[7] =  209.2124685808997
! c22938 = c22938b ! x[8] =  386.4424559553808
! c22938 = c22938b ! x[9] =  327.9904896071657
! c22938 = c22938b ! end of best known solution

End Equations
End Model
```

Stephan K.H. Seidl