tp055r.apm.m4

```Model tp055r
! Source version 2

! 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.
! With the macro defined, a relaxer, x[7], is furthermore introduced
! to reduce the high pressure of the linear equality restrictions.
! With such a decline in rank, the model is processed very quickly
! and precisely.

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

Parameters
lbx3hs = 0
lbx3r  = 1 ! increased lower bound prevents lingering at 20/3
lbx3   = ifelse(stricths,1,`lbx3hs',`lbx3r')
End Parameters

Variables
x[1] = 1, >=    0, <= 1
x[2] = 2, >=    0
x[3] = 0, >= lbx3
x[4] = 0, >=    0, <= 1
x[5] = 0, >=    0
x[6] = 2, >=    0
ifelse(stricths,1,`',`x[7] = 0')
obj
End Variables

Equations
ifelse(stricths,1,`',`x[7] +') x[1] + 2*x[2] + 5*x[5] - 6 = 0
ifelse(stricths,1,`',`x[7] +') x[1] + x[2] + x[3] - 3 = 0
ifelse(stricths,1,`',`x[7] +') x[4] + x[5] + x[6] - 2 = 0
ifelse(stricths,1,`',`x[7] +') x[1] + x[4] - 1 = 0
ifelse(stricths,1,`',`x[7] +') x[2] + x[5] - 2 = 0
ifelse(stricths,1,`',`x[7] +') x[3] + x[6] - 2 = 0

obj = x[1] + 2*x[2] + 4*x[5] + &
exp(x[1]*x[4]) ifelse(stricths,1,`',`+ x[7]^2')

! best known objective = 19/3 = 6.333333333333333
! begin of best known solution belonging to the revised case
! x[1] = 0
! x[2] = 4/3 = 1.333333333333333
! x[3] = 5/3 = 1.666666666666667
! x[4] = 1
! x[5] = 2/3 = 0.6666666666666667
! x[6] = 1/3 = 0.3333333333333333
! end of best known solution belonging to the revised case
End Equations
End Model
```

Stephan K.H. Seidl