public override EndCriteria.Type minimize(Problem P, EndCriteria endCriteria)
{
// set up of the problem
//double ftol = endCriteria.functionEpsilon(); // end criteria on f(x) (see Numerical Recipes in C++, p.410)
double xtol = endCriteria.rootEpsilon(); // end criteria on x (see GSL v. 1.9, http://www.gnu.org/software/gsl/)
int maxStationaryStateIterations_ = endCriteria.maxStationaryStateIterations();
EndCriteria.Type ecType = EndCriteria.Type.None;
P.reset();
Vector x_ = P.currentValue();
int iterationNumber_ = 0;
// Initialize vertices of the simplex
bool end = false;
int n = x_.Count;
vertices_ = new InitializedList <Vector>(n + 1, x_);
for (int i = 0; i < n; i++)
{
Vector direction = new Vector(n, 0.0);
Vector vertice = vertices_[i + 1];
direction[i] = 1.0;
P.constraint().update(ref vertice, direction, lambda_);
vertices_[i + 1] = vertice;
}
// Initialize function values at the vertices of the simplex
values_ = new Vector(n + 1, 0.0);
for (int i = 0; i <= n; i++)
{
values_[i] = P.value(vertices_[i]);
}
// Loop looking for minimum
do
{
sum_ = new Vector(n, 0.0);
for (int i = 0; i <= n; i++)
{
sum_ += vertices_[i];
}
// Determine the best (iLowest), worst (iHighest)
// and 2nd worst (iNextHighest) vertices
int iLowest = 0;
int iHighest;
int iNextHighest;
if (values_[0] < values_[1])
{
iHighest = 1;
iNextHighest = 0;
}
else
{
iHighest = 0;
iNextHighest = 1;
}
for (int i = 1; i <= n; i++)
{
if (values_[i] > values_[iHighest])
{
iNextHighest = iHighest;
iHighest = i;
}
else
{
if ((values_[i] > values_[iNextHighest]) && i != iHighest)
{
iNextHighest = i;
}
}
if (values_[i] < values_[iLowest])
{
iLowest = i;
}
}
// Now compute accuracy, update iteration number and check end criteria
// GSL exit strategy on x (see GSL v. 1.9, http://www.gnu.org/software/gsl
double simplexSize = Utils.computeSimplexSize(vertices_);
++iterationNumber_;
if (simplexSize < xtol || endCriteria.checkMaxIterations(iterationNumber_, ref ecType))
{
endCriteria.checkStationaryPoint(0.0, 0.0, ref maxStationaryStateIterations_, ref ecType);
endCriteria.checkMaxIterations(iterationNumber_, ref ecType);
x_ = vertices_[iLowest];
double low = values_[iLowest];
P.setFunctionValue(low);
P.setCurrentValue(x_);
return(ecType);
}
// If end criteria is not met, continue
double factor = -1.0;
double vTry = extrapolate(ref P, iHighest, ref factor);
if ((vTry <= values_[iLowest]) && (factor.IsEqual(-1.0)))
{
factor = 2.0;
extrapolate(ref P, iHighest, ref factor);
}
else if (Math.Abs(factor) > Const.QL_EPSILON)
{
if (vTry >= values_[iNextHighest])
{
double vSave = values_[iHighest];
factor = 0.5;
vTry = extrapolate(ref P, iHighest, ref factor);
if (vTry >= vSave && Math.Abs(factor) > Const.QL_EPSILON)
{
for (int i = 0; i <= n; i++)
{
if (i != iLowest)
{
#if QL_ARRAY_EXPRESSIONS
vertices_[i] = 0.5 * (vertices_[i] + vertices_[iLowest]);
#else
vertices_[i] += vertices_[iLowest];
vertices_[i] *= 0.5;
#endif
values_[i] = P.value(vertices_[i]);
}
}
}
}
}
// If can't extrapolate given the constraints, exit
if (Math.Abs(factor) <= Const.QL_EPSILON)
{
x_ = vertices_[iLowest];
double low = values_[iLowest];
P.setFunctionValue(low);
P.setCurrentValue(x_);
return(EndCriteria.Type.StationaryFunctionValue);
}
}while (end == false);
Utils.QL_FAIL("optimization failed: unexpected behaviour");
return(0);
}
public override EndCriteria.Type minimize(Problem P, EndCriteria endCriteria)
{
// Initializations
double ftol = endCriteria.functionEpsilon();
int maxStationaryStateIterations_ = endCriteria.maxStationaryStateIterations();
EndCriteria.Type ecType = EndCriteria.Type.None; // reset end criteria
P.reset(); // reset problem
Vector x_ = P.currentValue(); // store the starting point
int iterationNumber_ = 0;
// dimension line search
lineSearch_.searchDirection = new Vector(x_.size());
bool done = false;
// function and squared norm of gradient values
double fnew, fold, gold2;
double fdiff;
// classical initial value for line-search step
double t = 1.0;
// Set gradient g at the size of the optimization problem
// search direction
int sz = lineSearch_.searchDirection.size();
Vector prevGradient = new Vector(sz), d = new Vector(sz), sddiff = new Vector(sz), direction = new Vector(sz);
// Initialize cost function, gradient prevGradient and search direction
P.setFunctionValue(P.valueAndGradient(ref prevGradient, x_));
P.setGradientNormValue(Vector.DotProduct(prevGradient, prevGradient));
lineSearch_.searchDirection = prevGradient * -1;
bool first_time = true;
// Loop over iterations
do
{
// Linesearch
if (!first_time)
{
prevGradient = lineSearch_.lastGradient();
}
t = (lineSearch_.value(P, ref ecType, endCriteria, t));
// don't throw: it can fail just because maxIterations exceeded
if (lineSearch_.succeed())
{
// Updates
// New point
x_ = lineSearch_.lastX();
// New function value
fold = P.functionValue();
P.setFunctionValue(lineSearch_.lastFunctionValue());
// New gradient and search direction vectors
// orthogonalization coef
gold2 = P.gradientNormValue();
P.setGradientNormValue(lineSearch_.lastGradientNorm2());
// conjugate gradient search direction
direction = getUpdatedDirection(P, gold2, prevGradient);
sddiff = direction - lineSearch_.searchDirection;
lineSearch_.searchDirection = direction;
// Now compute accuracy and check end criteria
// Numerical Recipes exit strategy on fx (see NR in C++, p.423)
fnew = P.functionValue();
fdiff = 2.0 * Math.Abs(fnew - fold) /
(Math.Abs(fnew) + Math.Abs(fold) + Const.QL_EPSILON);
if (fdiff < ftol ||
endCriteria.checkMaxIterations(iterationNumber_, ref ecType))
{
endCriteria.checkStationaryFunctionValue(0.0, 0.0, ref maxStationaryStateIterations_, ref ecType);
endCriteria.checkMaxIterations(iterationNumber_, ref ecType);
return(ecType);
}
P.setCurrentValue(x_); // update problem current value
++iterationNumber_; // Increase iteration number
first_time = false;
}
else
{
done = true;
}
}while (!done);
P.setCurrentValue(x_);
return(ecType);
}
