//! Perform line search
public override double value(Problem P, ref EndCriteria.Type ecType, EndCriteria endCriteria, double t_ini)
{
//OptimizationMethod& method = P.method();
Constraint constraint = P.constraint();
succeed_ = true;
bool maxIter = false;
double qtold;
double t = t_ini;
int loopNumber = 0;
double q0 = P.functionValue();
double qp0 = P.gradientNormValue();
qt_ = q0;
qpt_ = (gradient_.Count == 0) ? qp0 : -Vector.DotProduct(gradient_, searchDirection_);
// Initialize gradient
gradient_ = new Vector(P.currentValue().Count);
// Compute new point
xtd_ = (Vector)P.currentValue().Clone();
t = update(ref xtd_, searchDirection_, t, constraint);
// Compute function value at the new point
qt_ = P.value(xtd_);
// Enter in the loop if the criterion is not satisfied
if ((qt_ - q0) > -alpha_ * t * qpt_)
{
do
{
loopNumber++;
// Decrease step
t *= beta_;
// Store old value of the function
qtold = qt_;
// New point value
xtd_ = P.currentValue();
t = update(ref xtd_, searchDirection_, t, constraint);
// Compute function value at the new point
qt_ = P.value(xtd_);
P.gradient(gradient_, xtd_);
// and it squared norm
maxIter = endCriteria.checkMaxIterations(loopNumber, ref ecType);
} while ((((qt_ - q0) > (-alpha_ * t * qpt_)) || ((qtold - q0) <= (-alpha_ * t * qpt_ / beta_))) && (!maxIter));
}
if (maxIter)
{
succeed_ = false;
}
// Compute new gradient
P.gradient(gradient_, xtd_);
// and it squared norm
qpt_ = Vector.DotProduct(gradient_, gradient_);
// Return new step value
return(t);
}
private double extrapolate(ref Problem P, int iHighest, ref double factor)
{
Vector pTry;
do
{
int dimensions = values_.Count - 1;
double factor1 = (1.0 - factor) / dimensions;
double factor2 = factor1 - factor;
pTry = sum_ * factor1 - vertices_[iHighest] * factor2;
factor *= 0.5;
}while (!P.constraint().test(pTry) && Math.Abs(factor) > Const.QL_EPSILON);
if (Math.Abs(factor) <= Const.QL_EPSILON)
{
return(values_[iHighest]);
}
factor *= 2.0;
double vTry = P.value(pTry);
if (vTry < values_[iHighest])
{
values_[iHighest] = vTry;
sum_ += pTry - vertices_[iHighest];
vertices_[iHighest] = pTry;
}
return(vTry);
}
//! Perform line search
public override double value(Problem P, ref EndCriteria.Type ecType, EndCriteria endCriteria, double t_ini) {
//OptimizationMethod& method = P.method();
Constraint constraint = P.constraint();
succeed_ = true;
bool maxIter = false;
double qtold;
double t = t_ini;
int loopNumber = 0;
double q0 = P.functionValue();
double qp0 = P.gradientNormValue();
qt_ = q0;
qpt_ = (gradient_.Count == 0) ? qp0 : -Vector.DotProduct(gradient_, searchDirection_);
// Initialize gradient
gradient_ = new Vector(P.currentValue().Count);
// Compute new point
xtd_ = (Vector)P.currentValue().Clone();
t = update(ref xtd_, searchDirection_, t, constraint);
// Compute function value at the new point
qt_ = P.value(xtd_);
// Enter in the loop if the criterion is not satisfied
if ((qt_ - q0) > -alpha_ * t * qpt_) {
do {
loopNumber++;
// Decrease step
t *= beta_;
// Store old value of the function
qtold = qt_;
// New point value
xtd_ = P.currentValue();
t = update(ref xtd_, searchDirection_, t, constraint);
// Compute function value at the new point
qt_ = P.value(xtd_);
P.gradient(gradient_, xtd_);
// and it squared norm
maxIter = endCriteria.checkMaxIterations(loopNumber, ref ecType);
} while ((((qt_ - q0) > (-alpha_ * t * qpt_)) || ((qtold - q0) <= (-alpha_ * t * qpt_ / beta_))) && (!maxIter));
}
if (maxIter)
succeed_ = false;
// Compute new gradient
P.gradient(gradient_, xtd_);
// and it squared norm
qpt_ = Vector.DotProduct(gradient_, gradient_);
// Return new step value
return t;
}
protected void amotsa(Problem P, double fac)
{
fac1_ = (1.0 - fac) / Convert.ToDouble(n_);
fac2_ = fac1_ - fac;
for (j_ = 0; j_ < n_; j_++)
{
ptry_[j_] = sum_[j_] * fac1_ - vertices_[ihi_][j_] * fac2_;
}
if (!P.constraint().test(ptry_))
{
ytry_ = Double.MaxValue;
}
else
{
ytry_ = P.value(ptry_);
}
if (Double.IsNaN(ytry_))
{
ytry_ = Double.MaxValue;
}
if (ytry_ <= yb_)
{
yb_ = ytry_;
pb_ = ptry_;
}
yflu_ = ytry_ - tt_ * Math.Log(rng_.next().value);
if (yflu_ < yhi_)
{
values_[ihi_] = ytry_;
yhi_ = yflu_;
for (j_ = 0; j_ < n_; j_++)
{
sum_[j_] += ptry_[j_] - vertices_[ihi_][j_];
vertices_[ihi_][j_] = ptry_[j_];
}
}
ytry_ = yflu_;
}
private double extrapolate(ref Problem P, int iHighest, ref double factor)
{
Vector pTry;
do
{
int dimensions = values_.Count - 1;
double factor1 = (1.0 - factor) / dimensions;
double factor2 = factor1 - factor;
// #if QL_ARRAY_EXPRESSIONS
pTry = sum_ * factor1 - vertices_[iHighest] * factor2;
//#else
// // composite expressions fail to compile with gcc 3.4 on windows
// pTry = sum_ * factor1;
// pTry -= vertices_[iHighest] * factor2;
//#endif
factor *= 0.5;
} while (!P.constraint().test(pTry) && Math.Abs(factor) > Const.QL_EPSILON);
if (Math.Abs(factor) <= Const.QL_EPSILON)
{
return(values_[iHighest]);
}
factor *= 2.0;
double vTry = P.value(pTry);
if (vTry < values_[iHighest])
{
values_[iHighest] = vTry;
//#if QL_ARRAY_EXPRESSIONS
sum_ += pTry - vertices_[iHighest];
//#else
// sum_ += pTry;
// sum_ -= vertices_[iHighest];
//#endif
vertices_[iHighest] = pTry;
}
return(vTry);
}
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
//// Numerical Recipes exit strategy on fx (see NR in C++, p.410)
//double low = values_[iLowest];
//double high = values_[iHighest];
//double rtol = 2.0*std::fabs(high - low)/
// (std::fabs(high) + std::fabs(low) + QL_EPSILON);
//++iterationNumber_;
//if (rtol < ftol ||
// endCriteria.checkMaxIterations(iterationNumber_, ecType)) {
// 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 == -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);
throw new Exception("optimization failed: unexpected behaviour");
}
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);
direction[i] = 1.0;
P.constraint().update(vertices_[i + 1], direction, lambda_);
}
// 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
//// Numerical Recipes exit strategy on fx (see NR in C++, p.410)
//double low = values_[iLowest];
//double high = values_[iHighest];
//double rtol = 2.0*std::fabs(high - low)/
// (std::fabs(high) + std::fabs(low) + QL_EPSILON);
//++iterationNumber_;
//if (rtol < ftol ||
// endCriteria.checkMaxIterations(iterationNumber_, ecType)) {
// 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 == -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);
throw new ApplicationException("optimization failed: unexpected behaviour");
}
private double extrapolate(ref Problem P, int iHighest, ref double factor)
{
Vector pTry;
do
{
int dimensions = values_.Count - 1;
double factor1 = (1.0 - factor) / dimensions;
double factor2 = factor1 - factor;
// #if QL_ARRAY_EXPRESSIONS
pTry = sum_ * factor1 - vertices_[iHighest] * factor2;
//#else
// // composite expressions fail to compile with gcc 3.4 on windows
// pTry = sum_ * factor1;
// pTry -= vertices_[iHighest] * factor2;
//#endif
factor *= 0.5;
} while (!P.constraint().test(pTry) && Math.Abs(factor) > Const.QL_Epsilon);
if (Math.Abs(factor) <= Const.QL_Epsilon)
{
return values_[iHighest];
}
factor *= 2.0;
double vTry = P.value(pTry);
if (vTry < values_[iHighest])
{
values_[iHighest] = vTry;
//#if QL_ARRAY_EXPRESSIONS
sum_ += pTry - vertices_[iHighest];
//#else
// sum_ += pTry;
// sum_ -= vertices_[iHighest];
//#endif
vertices_[iHighest] = pTry;
}
return vTry;
}
public override EndCriteria.Type minimize(Problem P, EndCriteria endCriteria)
{
int stationaryStateIterations_ = 0;
EndCriteria.Type ecType = EndCriteria.Type.None;
P.reset();
Vector x = P.currentValue();
iteration_ = 0;
n_ = x.size();
ptry_ = new Vector(n_, 0.0);
// build vertices
vertices_ = new InitializedList <Vector>(n_ + 1, x);
for (i_ = 0; i_ < n_; i_++)
{
Vector direction = new Vector(n_, 0.0);
direction[i_] = 1.0;
Vector tmp = vertices_[i_ + 1];
P.constraint().update(ref tmp, direction, lambda_);
vertices_[i_ + 1] = tmp;
}
values_ = new Vector(n_ + 1, 0.0);
for (i_ = 0; i_ <= n_; i_++)
{
if (!P.constraint().test(vertices_[i_]))
{
values_[i_] = Double.MaxValue;
}
else
{
values_[i_] = P.value(vertices_[i_]);
}
if (Double.IsNaN(ytry_))
{
// handle NAN
values_[i_] = Double.MaxValue;
}
}
// minimize
T_ = T0_;
yb_ = Double.MaxValue;
pb_ = new Vector(n_, 0.0);
do
{
iterationT_ = iteration_;
do
{
sum_ = new Vector(n_, 0.0);
for (i_ = 0; i_ <= n_; i_++)
{
sum_ += vertices_[i_];
}
tt_ = -T_;
ilo_ = 0;
ihi_ = 1;
ynhi_ = values_[0] + tt_ * Math.Log(rng_.next().value);
ylo_ = ynhi_;
yhi_ = values_[1] + tt_ * Math.Log(rng_.next().value);
if (ylo_ > yhi_)
{
ihi_ = 0;
ilo_ = 1;
ynhi_ = yhi_;
yhi_ = ylo_;
ylo_ = ynhi_;
}
for (i_ = 2; i_ < n_ + 1; i_++)
{
yt_ = values_[i_] + tt_ * Math.Log(rng_.next().value);
if (yt_ <= ylo_)
{
ilo_ = i_;
ylo_ = yt_;
}
if (yt_ > yhi_)
{
ynhi_ = yhi_;
ihi_ = i_;
yhi_ = yt_;
}
else
{
if (yt_ > ynhi_)
{
ynhi_ = yt_;
}
}
}
// GSL end criterion in x (cf. above)
if (endCriteria.checkStationaryPoint(simplexSize(), 0.0,
ref stationaryStateIterations_,
ref ecType) ||
endCriteria.checkMaxIterations(iteration_, ref ecType))
{
// no matter what, we return the best ever point !
P.setCurrentValue(pb_);
P.setFunctionValue(yb_);
return(ecType);
}
iteration_ += 2;
amotsa(P, -1.0);
if (ytry_ <= ylo_)
{
amotsa(P, 2.0);
}
else
{
if (ytry_ >= ynhi_)
{
ysave_ = yhi_;
amotsa(P, 0.5);
if (ytry_ >= ysave_)
{
for (i_ = 0; i_ < n_ + 1; i_++)
{
if (i_ != ilo_)
{
for (j_ = 0; j_ < n_; j_++)
{
sum_[j_] = 0.5 * (vertices_[i_][j_] +
vertices_[ilo_][j_]);
vertices_[i_][j_] = sum_[j_];
}
values_[i_] = P.value(sum_);
}
}
iteration_ += n_;
for (i_ = 0; i_ < n_; i_++)
{
sum_[i_] = 0.0;
}
for (i_ = 0; i_ <= n_; i_++)
{
sum_ += vertices_[i_];
}
}
}
else
{
iteration_ += 1;
}
}
}while (iteration_ <
iterationT_ + (scheme_ == Scheme.ConstantFactor ? m_ : 1));
switch (scheme_)
{
case Scheme.ConstantFactor:
T_ *= (1.0 - epsilon_);
break;
case Scheme.ConstantBudget:
if (iteration_ <= K_)
{
T_ = T0_ *
Math.Pow(1.0 - Convert.ToDouble(iteration_) / Convert.ToDouble(K_), alpha_);
}
else
{
T_ = 0.0;
}
break;
}
}while (true);
}