netgen/libsrc/opti/opti.hpp
Joachim Schoeberl 310cb00b13 autotools
2009-01-12 23:40:13 +00:00

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#ifndef FILE_OPTI
#define FILE_OPTI
/**************************************************************************/
/* File: opti.hpp */
/* Author: Joachim Schoeberl */
/* Date: 01. Jun. 95 */
/**************************************************************************/
namespace netgen
{
/**
Function to be minimized.
*/
class MinFunction
{
public:
///
virtual double Func (const Vector & x) const;
///
virtual void Grad (const Vector & x, Vector & g) const;
/// function and gradient
virtual double FuncGrad (const Vector & x, Vector & g) const;
/// directional derivative
virtual double FuncDeriv (const Vector & x, const Vector & dir, double & deriv) const;
/// if |g| < gradaccuray, then stop bfgs
virtual double GradStopping (const Vector & /* x */) const { return 0; }
///
virtual void ApproximateHesse (const Vector & /* x */,
DenseMatrix & /* hesse */) const;
};
class OptiParameters
{
public:
int maxit_linsearch;
int maxit_bfgs;
double typf;
double typx;
OptiParameters ()
{
maxit_linsearch = 100;
maxit_bfgs = 100;
typf = 1;
typx = 1;
}
};
/** Implementation of BFGS method.
Efficient method for non-linear minimiztion problems.
@param x initial value and solution
@param fun function to be minimized
*/
extern double BFGS (Vector & x, const MinFunction & fun,
const OptiParameters & par,
double eps = 1e-8);
/** Steepest descent method.
Simple method for non-linear minimization problems.
@param x initial value and solution
@param fun function to be minimized
*/
void SteepestDescent (Vector & x, const MinFunction & fun,
const OptiParameters & par);
extern void lines (
Vector & x, // i: Ausgangspunkt der Liniensuche
Vector & xneu, // o: Loesung der Liniensuche bei Erfolg
Vector & p, // i: Suchrichtung
double & f, // i: Funktionswert an der Stelle x
// o: Funktionswert an der Stelle xneu, falls ifail = 0
Vector & g, // i: Gradient an der Stelle x
// o: Gradient an der Stelle xneu, falls ifail = 0
const MinFunction & fun, // function to minmize
const OptiParameters & par, // parameters
double & alphahat, // i: Startwert f<>r alpha_hat
// o: Loesung falls ifail = 0
double fmin, // i: untere Schranke f<>r f
double mu1, // i: Parameter mu_1 aus Alg.2.1
double sigma, // i: Parameter sigma aus Alg.2.1
double xi1, // i: Parameter xi_1 aus Alg.2.1
double xi2, // i: Parameter xi_1 aus Alg.2.1
double tau, // i: Parameter tau aus Alg.2.1
double tau1, // i: Parameter tau_1 aus Alg.2.1
double tau2, // i: Parameter tau_2 aus Alg.2.1
int & ifail); // o: 0 bei erfolgreicher Liniensuche
// -1 bei Abbruch wegen Unterschreiten von fmin
// 1 bei Abbruch, aus sonstigen Gr<47>nden
/**
Solver for linear programming problem.
\begin{verbatim}
min c^t x
A x <= b
\end{verbatim}
*/
extern void LinearOptimize (const DenseMatrix & a, const Vector & b,
const Vector & c, Vector & x);
#ifdef NONE
/**
Simple projection iteration.
find $u = argmin_{v >= 0} 0.5 u A u - f u$
*/
extern void ApproxProject (const BaseMatrix & a, Vector & u,
const Vector & f,
double tau, int its);
/**
CG Algorithm for quadratic programming problem.
See: Dostal ...
d ... diag(A) ^{-1}
*/
extern void ApproxProjectCG (const BaseMatrix & a, Vector & x,
const Vector & b, const class DiagMatrix & d,
double gamma, int & steps, int & changes);
#endif
}
#endif