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OPT++

/** \page ConstraintsDoc  How to create constrained objects

<ul>
	<LI> \ref BoundConstraints
	<LI> \ref LinearConstraints
	<LI> \ref NonLinearConstraints
	<LI> \ref CompoundConstraintsDoc
</UL>
<p>
a constraint has finite lower and upper bounds, OPT++ treats it as two
separate constraints.  In the computation of the residuals and gradients
constraints with finite lower bounds appear first followed by those with
finte upper bounds. Consequently, in the optimization summary, you will
see the constraint count is double the original number of constraints.  
</p>

Now, we are ready to build an constrained nonlinear program.

Let's consider the two-dimensional Rosenbrock problem with bound constraints.

<em> minimize   </em> \f[100(x_2 - x_{1}^2)^2 + (1 - x_1)^2 \f]
<em> subject to </em>  \f[ -2.0 \le x \le 2.0\f] 

Step 1: Build your compound constraint.
\code
   int ndim =  2;
   ColumnVector lower(ndim), upper(ndim);
   lower    = -2.0;
   upper    =  2.0;

   Constraint bc = new BoundConstraint(ndim, lower, upper);
   CompoundConstraint* rosen_constraints = new CompoundConstraint(bc);
\endcode

Step 2: Create a nonlinear function with analytic derivatives. 
<ul>
	<li> First, write a function which initializes <em>x<sub>0</sub></em>. 
\code
   void init_rosen (int ndim, ColumnVector& x)
   {
      if (ndim != 2)
      {
	 exit (1);
      }
      x(1) = -1.2;
      x(2) =  1.0;
   }
\endcode
</li>
<li> Next, write a function that evaluates the Rosenbrock function 
and gradient.
\code
   void rosen(int mode, int n, const ColumnVector& x, double& fx, 
              ColumnVector& g, int& result)
   { // Rosenbrock's function
      double f1, f2, x1, x2;
    
      if (n != 2) return;

      x1 = x(1);
      x2 = x(2);
      f1 = (x2 - x1 * x1);
      f2 = 1. - x1;

      if (mode & NLPFunction) {
          fx  = 100.* f1*f1 + f2*f2;
      }
      if (mode & NLPGradient) {
         g(1) = -400.*f1*x1 - 2.*f2; 
         g(2) = 200.*f1;
      }
      result = NLPFunction & NLPGradient;
   }
\endcode
</li>
</ul>

Step 3: Create a constrained nonlinear problem with analytic derivatives 
\code
   NLF1 nips(n,rosen,init_rosen,rosen_constraints);
\endcode

Voila! You're done.
<p> <a href="ExamplesDoc.html">Next Section: Examples of test fragments</a> |  
<a href="index.html">Back to Main Page</a> </p> 

*/