boundconstraints.html.svn-base

OPT++

/** \page BoundConstraints  Constructing bound-constrained objects 

In OPT++, the standard form for a bound constraint is
\f[ x \ge  l. \f]

However, the user has the option of creating constraints with upper bounds 
or constraints with lower and upper bounds. The BoundConstraint class contains
four constructors.

The first constructor creates a bound constraint in standard form.
For example,
\code
   BoundConstraint(int nc, const ColumnVector& lower);
\endcode
where \a nc is the number of constraints, and \a lower is a 
vector that contains the lower bounds on the constraints.

To define upper bounds on the variables, such as
\f[ x \le  u, \f] use the following constructor:
\code
   BoundConstraint(int nc, const ColumnVector& bound, 
                   const BoolVector& bdFlag);
\endcode

Sample code to create \f[ x_i \le i, \forall i=1,2,..,5 \f] appears below. 
\code
   bool bdFlag;
   int numOfCons = 5;
   ColumnVector bound(numOfCons);
   bound  << 1.0 << 2.0 << 3.0
          << 4.0 << 5.0;
   bdFlag = false;
   BoundConstraint bc(numOfCons, bound, bdFlag); 
\endcode

To define lower and upper bounds on the variables,
use 
\code
   BoundConstraint(int nc, const ColumnVector& lower, 
      		   const ColumnVector& upper)
\endcode
which creates 
\f[l \le x \le u. \f]
By default, the first ColumnVector contains the lower bounds
and the second ColumnVector the upper bounds on the constraints.
<p>
OPT++ does not support sparse constraints.  Therefore, a bound must be given 
for each variable even if only a subset of the variables have finite bounds.
An infinite lower bound is specified by
\f[l_i \le -1.0e10. \f]
Similarly, an infinite upper bound is specified by
\f[u_i \ge  1.0e10. \f]
</p>

<p> <a href="LinearConstraints.html">Next Section: Constructing linear constraints
</a> | <a href="index.html">Back to Main Page</a> </p> 

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