/** \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.

- \ref UnconstrainedObject
- \ref UnconstrainedDefn
- \ref UnconstrainedFragments

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

1. \ref tstcg
2. \ref tstqnewton

Next Section: Bound-constrained Minimization | Back to Solvers Page

Last revised July 13, 2006 */