### tp117r2.apm.m4

```Model tp117r2
! Source version 1

! This is a condensed formulation of #117r for human readers.
! The present file has to be drawn through the m4 macro processor
! at first, with or without `-Drevisedhs'. With the macro
! defined, the feasible domain is reduced in comparison with the H+S
! one such that some unwanted secondary minimum is excluded.

ifdef(`revisedhs',`define(`stricths',0)',`define(`stricths',1)')

Parameters
a24a = 4/10 ! from PROB.FOR
a24b = 4    ! from H+S, seems to be a typo
a24  = a24a ! my decision is irrelevant,
! a24 appears as a summand (-1)*a24*x[2] in c[4]
! and x[2] is going to vanish
ivxhs[1: 6] =  0.001
ivxhs[7: 7] = 60
ivxhs[8:15] =  0.001
lbx[ 1] = ifelse(stricths,1,`0',`0')
lbx[ 2] = ifelse(stricths,1,`0',`0')
lbx[ 3] = ifelse(stricths,1,`0',`1')
lbx[ 4] = ifelse(stricths,1,`0',`0')
lbx[ 5] = ifelse(stricths,1,`0',`1')
lbx[ 6] = ifelse(stricths,1,`0',`1')
lbx[ 7] = ifelse(stricths,1,`0',`0')
lbx[ 8] = ifelse(stricths,1,`0',`0')
lbx[ 9] = ifelse(stricths,1,`0',`0.09')
lbx[10] = ifelse(stricths,1,`0',`0')
lbx[11] = ifelse(stricths,1,`0',`0.1')
lbx[12] = ifelse(stricths,1,`0',`0.3')
lbx[13] = ifelse(stricths,1,`0',`0.3')
lbx[14] = ifelse(stricths,1,`0',`0.2')
lbx[15] = ifelse(stricths,1,`0',`0.1')
! make the initial point feasible
! ivx[1:15] = max(ivxhs[1:15],lbx[1:15])
! max() expressed by abs() for APMonitor
ivx[1:15] = (1/2)*(abs(ivxhs[1:15] - lbx[1:15]) + &
(ivxhs[1:15] + lbx[1:15]))
End Parameters

Variables
x[1:15] = ivx[1:15], >= lbx[1:15]
obj
End Variables

Intermediates
c[1] = (-15) + 16*x[1] + (7/2)*x[3] - 2*x[6] + x[7] + x[8]       &
- x[9] - x[10] + 60*x[11] - 40*x[12] - 20*x[13] + 64*x[14]  &
- 20*x[15] + 12*x[11]^2
c[2] = (-27) - 2*x[1] + 2*x[2] + 2*x[4] + 9*x[5] + x[7] + 2*x[8] &
- 2*x[9] - x[10] - 40*x[11] + 78*x[12] - 12*x[13]           &
- 62*x[14] + 64*x[15] + 24*x[12]^2
c[3] = (-36) - 2*x[3] + 2*x[5] + 4*x[6] + x[7] + 3*x[8] - 3*x[9] &
- x[10] - 20*x[11] - 12*x[12] + 20*x[13] - 12*x[14]         &
- 20*x[15] + 30*x[13]^2
c[4] = (-18) - x[1] - a24*x[2] + 4*x[4] - x[5] + x[7] + 2*x[8]   &
- 4*x[9] - x[10] + 64*x[11] - 62*x[12] - 12*x[13]           &
+ 78*x[14] - 40*x[15] + 18*x[14]^2
c[5] = (-12) - 2*x[2] + x[4] + (14/5)*x[5] + x[7] + x[8]         &
- 5*x[9] - x[10] - 20*x[11] + 64*x[12] - 20*x[13]           &
- 40*x[14] + 60*x[15] + 6*x[15]^2
mf   = 40*x[1] + 2*x[2] + (1/4)*x[3] + 4*x[4] + 4*x[5] + x[6]    &
+ 40*x[7] + 60*x[8] - 5*x[9] - x[10] + 30*x[11]^2           &
- 40*x[11]*x[12] - 20*x[11]*x[13] + 64*x[11]*x[14]          &
- 20*x[11]*x[15] + 39*x[12]^2 - 12*x[12]*x[13]              &
- 62*x[12]*x[14] + 64*x[12]*x[15] + 10*x[13]^2              &
- 12*x[13]*x[14] - 20*x[13]*x[15] + 39*x[14]^2              &
- 40*x[14]*x[15] + 30*x[15]^2 + 8*x[11]^3 + 16*x[12]^3      &
+ 20*x[13]^3 + 12*x[14]^3 + 4*x[15]^3
End Intermediates

Equations
c[1:5] >= 0

obj = mf

! best known objective = 32.34867896572271
! begin of best known solution belonging to the revised case
! x[ 1] =  0
! x[ 2] =  0
! x[ 3] =  5.174040727698173
! x[ 4] =  0
! x[ 5] =  3.06110868775845
! x[ 6] = 11.83954566480073
! x[ 7] =  0
! x[ 8] =  0
! x[ 9] =  0.1038961907706158
! x[10] =  0
! x[11] =  0.3
! x[12] =  0.3334676065346071
! x[13] =  0.4
! x[14] =  0.4283101047816988
! x[15] =  0.2239648735607981
! end of best known solution belonging to the revised case
End Equations
End Model
```

Stephan K.H. Seidl