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OPT++

/** \page BoundConstrainedProblems  Bound-constrained minimization 

In this section, we describe the framework for a bound-constrained
minimization problem.  
<UL>
<li> \ref  BoundConstraints
<li> \ref  BCProblem
<li> \ref  BCFragments
</UL>

\section BCProblem Creating a bound-constrained nonlinear problem 
Once you have mastered bound-constrained objects and setting up the objective
function, it is a simple 2-step process to build a bound-constrained 
nonlinear problem. 

Let's consider the two-dimensional Rosenbrock problem with bounds on
the variables: 

<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_1 \le 2.0 \f] 
<em>  </em>  \f[ -2.0 \le x_2 \le 2.0 \f] 

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

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

Step 2: Create a constrained NLF1 object.
\code
   NLF1 rosen_problem(n,rosen,init_rosen,&bc);
\endcode

\section BCFragments  Specifying the optimization method 
OPT++ contains no less than six solvers for bound-constrained optimization
problems.  To name a few, there are implementations of Newton's method, 
barrier Newton's method, interior-point methods, and direct search algorithms.
We provide examples of solving the bound-constrained Rosenbrock problem 
with an active set strategy and a nonlinear interior-point method. 
<ol>
	<li> \ref tstbcqnewton
	<li> \ref tstbcnips
</ol>

<p> <a href="ConstrainedProblems.html">
	Next Section: Constrained minimization
</a> |  <a href="Classification.html">Back to Solvers Page</a> </p> 

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