This piece of software implements an Augmented Lagrangian method 
described in [1]. This particular implementation, specially designed 
for small to medium scale problems solves the Augmented Lagrangian 
subproblems using the method BETRA introduced in [2]. BETRA is an 
active-set method for bound constrained minimization. It uses 
Spectral Projected Gradients to leave the faces and a trust regions 
method in the inner iterations. 

[1] R. Andreani, E. G. Birgin, J. M. Martínez and M. L. Schuverdt, 
"On Augmented Lagrangian methods with general lower-level constraints", 
submitted, 2005.

[2] M. Andretta, E. G. Birgin and J. M. Martínez, "Practical active-set 
Euclidian trust-region method with spectral projected gradients for 
bound-constrained minimization", Optimization 54, pp. 305-325, 2005.

Description of the files:

albetra.for  : implements the optimization method,

albetra.out  : is the output of the optimization method for a very easy 
               problem,

solution.txt : the solution of this easy problem found by ALBETRA.

For an easy test copy the file albetra.for. Compile typing

f77 -O4 albetra.for -o albetra

and execute typing

albetra.

The output that will appear in the screen will be the application of ALBETRA
to a very easy problem implemented in subroutines

inip    : set the number of variables, the number of constraints, the bounds
          the initial points and other few parameters of the problem,

evalf   : computes the objective function,

evalg   : computes the gradient of the objective funtion,

evalh   : computes the Hessian of the objective funtion,

evalc   : computes the constraints,

evaljac : computes the gradients of the constraints, and

evalch  : computes the Hessians of the constraints.

Solution will be saved in the output file solution.txt. Moreover, everything
that appears in the screen will be also saved in the file albetra.out. All 
the subroutines described above can be easily modified to solve your own 
problem.