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OPT++

/** \page UnconstrainedProblems  Unconstrained minimization 

In this section, we present the constructors for an objective function,
supply a prototype function evaluator, and provide examples for 
solving the unconstrained minimization problem. 

<UL>
<li> \ref  UnconstrainedObject
<li> \ref  UnconstrainedDefn
<li> \ref  UnconstrainedFragments
</UL>

\section UnconstrainedDefn Defining an unconstrained problem 
Let's consider the two-dimensional Rosenbrock problem with analytic derivatives.

<em> minimize   </em> \f$100(x_2 - x_{1}^2)^2 + (1 - x_1)^2 \f$

Representing the Rosenbrock problem as an NLF1 requires an 
user-supplied function to evaluate the problem and construction of an NLF1.

Step 1: Write a function that evaluates the Rosenbrock problem 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

Step 2: Create an NLF1 object.
\code
   NLF1 rosen_problem(n,rosen,init_rosen);
\endcode

\section UnconstrainedFragments  Specifying the optimization method 
There are several algorithms in OPT++ to solve unconstrained problems.
We provide examples of solving the Rosenbrock problem with a conjugate 
gradient and Quasi-Newton method.

<ol>
	<li> \ref tstcg
	<li> \ref tstqnewton
</ol>

<p> <a href="BoundConstrainedProblems.html">
	Next Section: Bound-constrained Minimization
</a> |  <a href="Classification.html">Back to Solvers Page</a> </p> 

Last revised <em> July 13, 2006</em>

*/