### apm/tp113.apm

```Model tp113
! Source version 1
! Simple APM canonicalizer version 1.3
! APM backend version 1.1
Parameters
End Parameters
Variables
x_1 = 2
x_2 = 3
x_3 = 5
x_4 = 5
x_5 = 1
x_6 = 2
x_7 = 7
x_8 = 3
x_9 = 6
x_10 = 10
obj
End Variables
Intermediates
c_1 = 105 - 4*x_1 - 5*x_2 + 3*x_7 - 9*x_8
c_2 = (-1)*10*x_1 + 8*x_2 + 17*x_7 - 2*x_8
c_3 = 8*x_1 - 2*x_2 - 5*x_9 + 2*x_10 + 12
c_4 = (-3)*(x_1 - 2)^2 - 4*(x_2 - 3)^2 - 2*x_3^2 + 7*x_4 + 120
c_5 = (-5)*x_1^2 - 8*x_2 - (x_3 - 6)^2 + 2*x_4 + 40
c_6 = (-1/2)*(x_1 - 8)^2 - 2*(x_2 - 4)^2 - 3*x_5^2 + x_6 + 30
c_7 = (-1)*x_1^2 - 2*(x_2 - 2)^2 + 2*x_1*x_2 - 14*x_5 + 6*x_6
c_8 = 3*x_1 - 6*x_2 - 12*(x_9 - 8)^2 + 7*x_10
mf = x_1^2 + x_2^2 + x_1*x_2 - 14*x_1 - 16*x_2 + (x_3 - 10)^2 + 4*(x_4 - 5)^2 + (x_5 - 3)^2 + 2*(x_6 - 1)^2 &
+ 5*x_7^2 + 7*(x_8 - 11)^2 + 2*(x_9 - 10)^2 + (x_10 - 7)^2 + 45
myminfun = mf
myabsdevnod0_0 = abs(myminfun - 24.30620906817981)
myreldevnod0_0 = abs(myminfun/24.30620906817981 - 1)
myabsdevnod0_1 = abs(x_1 - 2.171996371255455)
myreldevnod0_1 = abs(x_1/2.171996371255455 - 1)
myabsdevnod0_2 = abs(x_2 - 2.36368297369728)
myreldevnod0_2 = abs(x_2/2.36368297369728 - 1)
myabsdevnod0_3 = abs(x_3 - 8.77392573847685)
myreldevnod0_3 = abs(x_3/8.77392573847685 - 1)
myabsdevnod0_4 = abs(x_4 - 5.095984487948453)
myreldevnod0_4 = abs(x_4/5.095984487948453 - 1)
myabsdevnod0_5 = abs(x_5 - 0.9906547649638592)
myreldevnod0_5 = abs(x_5/0.9906547649638592 - 1)
myabsdevnod0_6 = abs(x_6 - 1.430573978936316)
myreldevnod0_6 = abs(x_6/1.430573978936316 - 1)
myabsdevnod0_7 = abs(x_7 - 1.321644208161703)
myreldevnod0_7 = abs(x_7/1.321644208161703 - 1)
myabsdevnod0_8 = abs(x_8 - 9.828725807886321)
myreldevnod0_8 = abs(x_8/9.828725807886321 - 1)
myabsdevnod0_9 = abs(x_9 - 8.280091670098346)
myreldevnod0_9 = abs(x_9/8.280091670098346 - 1)
myabsdevnod0_10 = abs(x_10 - 8.375926663921323)
myreldevnod0_10 = abs(x_10/8.375926663921323 - 1)
myabsdevnod1_0 = (1/2)*(abs(myabsdevnod0_0 - myabsdevnod0_1) + (myabsdevnod0_0 + myabsdevnod0_1))
myreldevnod1_0 = (1/2)*(abs(myreldevnod0_0 - myreldevnod0_1) + (myreldevnod0_0 + myreldevnod0_1))
myabsdevnod1_2 = (1/2)*(abs(myabsdevnod0_2 - myabsdevnod0_3) + (myabsdevnod0_2 + myabsdevnod0_3))
myreldevnod1_2 = (1/2)*(abs(myreldevnod0_2 - myreldevnod0_3) + (myreldevnod0_2 + myreldevnod0_3))
myabsdevnod1_4 = (1/2)*(abs(myabsdevnod0_4 - myabsdevnod0_5) + (myabsdevnod0_4 + myabsdevnod0_5))
myreldevnod1_4 = (1/2)*(abs(myreldevnod0_4 - myreldevnod0_5) + (myreldevnod0_4 + myreldevnod0_5))
myabsdevnod1_6 = (1/2)*(abs(myabsdevnod0_6 - myabsdevnod0_7) + (myabsdevnod0_6 + myabsdevnod0_7))
myreldevnod1_6 = (1/2)*(abs(myreldevnod0_6 - myreldevnod0_7) + (myreldevnod0_6 + myreldevnod0_7))
myabsdevnod1_8 = (1/2)*(abs(myabsdevnod0_8 - myabsdevnod0_9) + (myabsdevnod0_8 + myabsdevnod0_9))
myreldevnod1_8 = (1/2)*(abs(myreldevnod0_8 - myreldevnod0_9) + (myreldevnod0_8 + myreldevnod0_9))
myabsdevnod1_10 = myabsdevnod0_10
myreldevnod1_10 = myreldevnod0_10
myabsdevnod2_0 = (1/2)*(abs(myabsdevnod1_0 - myabsdevnod1_2) + (myabsdevnod1_0 + myabsdevnod1_2))
myreldevnod2_0 = (1/2)*(abs(myreldevnod1_0 - myreldevnod1_2) + (myreldevnod1_0 + myreldevnod1_2))
myabsdevnod2_4 = (1/2)*(abs(myabsdevnod1_4 - myabsdevnod1_6) + (myabsdevnod1_4 + myabsdevnod1_6))
myreldevnod2_4 = (1/2)*(abs(myreldevnod1_4 - myreldevnod1_6) + (myreldevnod1_4 + myreldevnod1_6))
myabsdevnod2_8 = (1/2)*(abs(myabsdevnod1_8 - myabsdevnod1_10) + (myabsdevnod1_8 + myabsdevnod1_10))
myreldevnod2_8 = (1/2)*(abs(myreldevnod1_8 - myreldevnod1_10) + (myreldevnod1_8 + myreldevnod1_10))
myabsdevnod3_0 = (1/2)*(abs(myabsdevnod2_0 - myabsdevnod2_4) + (myabsdevnod2_0 + myabsdevnod2_4))
myreldevnod3_0 = (1/2)*(abs(myreldevnod2_0 - myreldevnod2_4) + (myreldevnod2_0 + myreldevnod2_4))
myabsdevnod3_8 = myabsdevnod2_8
myreldevnod3_8 = myreldevnod2_8
myabsdevnod4_0 = (1/2)*(abs(myabsdevnod3_0 - myabsdevnod3_8) + (myabsdevnod3_0 + myabsdevnod3_8))
myreldevnod4_0 = (1/2)*(abs(myreldevnod3_0 - myreldevnod3_8) + (myreldevnod3_0 + myreldevnod3_8))
zmyabsdevmax = myabsdevnod4_0
zmyreldevmax = myreldevnod4_0
End Intermediates
Equations
obj = myminfun
c_1 >= 0
c_2 >= 0
c_3 >= 0
c_4 >= 0
c_5 >= 0
c_6 >= 0
c_7 >= 0
c_8 >= 0
End Equations
End Model
```

Stephan K.H. Seidl