private OptVector[] BuildMatrixA(
List <Func <double[], double> > equalityConstraints,
List <InequalityConstraintProperties> inequalityConstraints,
OptVector[] lagrangianHessian,
OptVector x)
{
List <OptVector> constraintDerivative = new List <OptVector>();
for (int i = 0; i < equalityConstraints.Count; i++)
{
constraintDerivative.Add(new OptVector(numericalDerivative.EvaluatePartialDerivative(equalityConstraints[i], x.MinArray, 1)));
}
for (int i = 0; i < inequalityConstraints.Count; i++)
{
if (inequalityConstraints[i].IsActive)
{
constraintDerivative.Add(new OptVector(numericalDerivative.EvaluatePartialDerivative(inequalityConstraints[i].Function, x.MinArray, 1)));
}
}
OptVector[] bufHessian = new OptVector[lagrangianHessian.Length];
OptVector[] modifiedLagrangian = OptVector.Sum(lagrangianHessian, epsilonNw);
Array.Copy(modifiedLagrangian, bufHessian, lagrangianHessian.Length);
for (int i = 0; i < bufHessian.Length; i++)
{
OptVector buf = new OptVector(constraintDerivative.Count);
for (int j = 0; j < constraintDerivative.Count; j++)
{
buf[j] = constraintDerivative[j][i];
}
bufHessian[i].Add(buf);
}
var lagrangianList = bufHessian.ToList();
foreach (var item in constraintDerivative)
{
var res = OptVector.Add(item, new OptVector(constraintDerivative.Count, -epsilonSe));
lagrangianList.Add(res);
}
return(lagrangianList.ToArray());
}
static void TestFunc()
{
OptVector a = new OptVector(new double[] { 1, 2 });
OptVector b = new OptVector(new double[] { 3, 4 });
OptVector c = new OptVector(new double[] { 1, 3 });
OptVector d = new OptVector(new double[] { 4, 7 });
var res = OptVector.Mult(a, b);
var res1 = OptVector.SubtractFromIdentity(res);
var res2 = OptVector.Div(res, 2);
OptVector[] aa = new OptVector[] { a, b };
OptVector[] bb = new OptVector[] { c, d };
var res3 = OptVector.Mult(res, bb);
var res4 = OptVector.Sum(res, bb);
var res5 = OptVector.Mult(res, c);
}
private OptVector[] CalculateLagrangianHessian(
Func <double[], double> lagrangian,
OptVector[] lagrangianHessian,
OptVector xNew,
OptVector xOld,
OptVector step)
{
OptVector s = step;
OptVector y = new OptVector(numericalDerivative.EvaluatePartialDerivative(lagrangian, xNew.MinArray, 1)) -
new OptVector(numericalDerivative.EvaluatePartialDerivative(lagrangian, xOld.MinArray, 1));
OptVector[] yy = OptVector.Mult(y, y);
double ys = y * s;
OptVector partialDenom = OptVector.Mult(lagrangianHessian, s);
OptVector[] num = OptVector.Mult(partialDenom, OptVector.Mult(s, lagrangianHessian));
double denom = -1.0 * s * partialDenom;
#region Positive definiteness
if (ys < 1E-15)
{
double theta = 0.999999;
OptVector yNew = new OptVector(y);
double ysNew = ys;
while (ysNew < lambda * s * partialDenom &&
theta >= 0.0)
{
yNew = y * theta + (1.0 - theta) * partialDenom;
ysNew = yNew * s;
theta = theta - 1E-5;
}
y = yNew;
ys = ysNew;
yy = OptVector.Mult(y, y);
}
#endregion
if (ys == 0.0)
{
if (step.Length() > 0)
{
return(OptVector.GetIdentity(xNew.Count, step));
}
return(OptVector.GetIdentity(xNew.Count));
}
OptVector[] addParam1 = OptVector.Div(yy, ys);
OptVector[] addParam2 = OptVector.Div(num, denom);
return(OptVector.Sum(OptVector.Sum(lagrangianHessian, addParam1), addParam2));
}
