### tp067v3.mac

```fmcTitle ("tp067v3")\$

/* Source version 2 */

/* FMC's second native input language.                      */
/* The Hock & Schittkowski test problem #67.                */
/* This is a free, more intuitive formulation of #67,       */
/* without discontinuities, as it would probably be defined */
/* by a modeler of our days.                                */
/* The solution is equal to the one obtained with tp067v1,  */
/* i.e., it is sensible but not exact in the sense of #67.  */

y2 : tp067v3x (fmc_ident_tcb, 2, 0, x1, x2, x3)\$
y3 : tp067v3x (fmc_ident_tcb, 3, 0, x1, x2, x3)\$
y4 : tp067v3x (fmc_ident_tcb, 4, 0, x1, x2, x3)\$
y5 : tp067v3x (fmc_ident_tcb, 5, 0, x1, x2, x3)\$
y6 : tp067v3x (fmc_ident_tcb, 6, 0, x1, x2, x3)\$
y7 : tp067v3x (fmc_ident_tcb, 7, 0, x1, x2, x3)\$
y8 : tp067v3x (fmc_ident_tcb, 8, 0, x1, x2, x3)\$

fmcFunctionDiffHint ([ tp067v3x, 0, 0, 0,
tp067v3x ( fmcFunctionArg1,  fmcFunctionArg2,  1,
fmcFunctionArg4,  fmcFunctionArg5,  fmcFunctionArg6 ),
tp067v3x ( fmcFunctionArg1,  fmcFunctionArg2,  2,
fmcFunctionArg4,  fmcFunctionArg5,  fmcFunctionArg6 ),
tp067v3x ( fmcFunctionArg1,  fmcFunctionArg2,  3,
fmcFunctionArg4,  fmcFunctionArg5,  fmcFunctionArg6 ) ])\$

fmcExternalCodePath ("../../doc/RevisedHockSchittkowski/src/tp067v3x.c")\$

fmcMinimum (-(0.063b0*y2*y5 - 5.04b0*x1 - 3.36b0*y3 - 0.035b0*x2 - 10*x3))\$

fmcInequality (i1,  y2 -     0)\$
fmcInequality (i2,  y3 -     0)\$
fmcInequality (i3,  y4 -    85)\$
fmcInequality (i4,  y5 -    90)\$
fmcInequality (i5,  y6 -     3)\$
fmcInequality (i6,  y7 - 1/100)\$
fmcInequality (i7,  y8 -   145)\$

fmcInequality (i8, 5000 - y2)\$
fmcInequality (i9, 2000 - y3)\$
fmcInequality (i10,  93 - y4)\$
fmcInequality (i11,  95 - y5)\$
fmcInequality (i12,  12 - y6)\$
fmcInequality (i13,   4 - y7)\$
fmcInequality (i14, 162 - y8)\$

fmcStrongLowerBound (x1, 10^(-5))\$
fmcStrongLowerBound (x2, 10^(-5))\$
fmcStrongLowerBound (x3, 10^(-5))\$

fmcStrongUpperBound (x1,  2000)\$
fmcStrongUpperBound (x2, 16000)\$
fmcStrongUpperBound (x3,   120)\$

fmcInitialValue (x1,  1745)\$
fmcInitialValue (x2, 12000)\$
fmcInitialValue (x3,   110)\$

/* best known objective = -1162.02698005969 */
/* begin of best known solution             */
/* x[1] = x1 =  1728.371443241086           */
/* x[2] = x2 = 16000                        */
/* x[3] = x3 =    98.13617652300942         */
/* end of best known solution               */
```

Stephan K.H. Seidl