# 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