# Examples¶

## Finding Minimum of the Gamma Function¶

The following model (gamma.mod) finds a minimum of the gamma function \(\Gamma(x)\) for \(x > 0\):

```
# Find minimum of the gamma function for x > 0.
include gsl.ampl;
var x >= 1e-5;
minimize obj: gsl_sf_gamma(x);
solve;
print x;
```

Solving this models gives an optimal solution \(x \approx 1.46163\) which can be verified here.

## Hock and Schittkowski Models¶

The hs068.mod and
hs069.mod
models demonstrate the use of `gsl_cdf_ugaussian_P()`

. They are taken
form the Robert Vanderbei’s collection of nonlinear models and adapted for AMPLGSL.
These models can be solved with a nonlinear AMPL solver such as MINOS:

```
$ ampl hs068.mod
obj = -0.261841
MINOS 5.51: optimal solution found.
29 iterations, objective -0.9204250037
Nonlin evals: obj = 57, grad = 56, constrs = 57, Jac = 56.
x [*] :=
1 0.0678586
2 3.64621
3 0.000266135
4 0.894855
;
obj = -0.920425
Best known objective value: -0.920425026
```