private static double LineSearch(ConstraintRefContainer cons, Vector xold, Vector s, double f1, double alpha2, double alpha1)
{
// //Take a step of alpha=1 as alpha2
var originalData = xold + alpha2 * s;
var f2 = cons.Calc(originalData);
// //Take a step of alpha 3 that is 2*alpha2
var alpha3 = alpha2 * 2;
originalData = xold + alpha3 * s;
var f3 = cons.Calc(originalData);
//Now reduce or lengthen alpha2 and alpha3 until the minimum is
//Bracketed by the triplet f1>f2<f3
while (f2 > f1 || f2 > f3)
{
if (f2 > f1)
{
//If f2 is greater than f1 then we shorten alpha2 and alpha3 closer to f1
//Effectively both are shortened by a factor of two.
alpha3 = alpha2;
f3 = f2;
alpha2 = alpha2 / 2;
originalData = xold + alpha2 * s;
f2 = cons.Calc(originalData);
}
else if (f2 > f3)
{
//If f2 is greater than f3 then we length alpah2 and alpha3 closer to f1
//Effectively both are lengthened by a factor of two.
alpha2 = alpha3;
f2 = f3;
alpha3 = alpha3 * 2;
originalData = xold + alpha3 * s;
f3 = cons.Calc(originalData);
}
}
// get the alpha for the minimum f of the quadratic approximation
var denominator = f1 - 2 * f2 + f3;
denominator = denominator < 1e-13 ? 1e-13 : denominator;
var alphaStar = alpha2 + ((alpha2 - alpha1) * (f1 - f3)) / (3 * denominator);
//Guarantee that the new alphaStar is within the bracket
if (alphaStar > alpha3 || alphaStar < alpha1)
{
alphaStar = alpha2;
}
return(alphaStar);
}
public int SolveRef(ref Vector originalData, int freeValuesCount, ConstraintRefContainer cons, double isFine)
{
var xLength = originalData.Count;
//Save the original parameters for later.
var origSolution1 = new Vector(originalData);
var convergence = isFine > 0.1 ? XconvergenceFine : XconvergenceRough;
//Calculate Function at the starting point:
var f0 = cons.Calc(originalData);
if (f0 < SmallF)
{
return(0);
}
//Calculate the gradient at the starting point:
var grad = new Vector(xLength); //The gradient vector (1xn)
for (var j = 0; j < freeValuesCount; j++)
{
grad[j] = cons.Grad(originalData, j);
}
//Initialize N and calculate s
var n = Matrix.Identity(xLength, xLength);
var s = -grad;
var fnew = f0 + 1;
var xold = new Vector(originalData); //Storage for the previous design variables
/////////////////////////////////////////////////////////
//// Calculate first step
/////////////////////////////////////////////////////////
//Make the initial position alpha1
double alpha1 = 0;
////Take a step of alpha=1 as alpha2
double alpha2 = 1;
double f1 = fnew;
var alphaStar = LineSearch(cons, xold, s, f1, alpha2, alpha1);
originalData = xold + alphaStar * s;
fnew = cons.Calc(originalData);
/////////////////////////////////////
// end of first step
/////////////////////////////////////
var deltaX = new Vector(xLength);
var gradnew = new Vector(xLength);
double deltaXnorm = 1;
var iterations = 1;
deltaX = originalData - xold;
while (deltaXnorm > convergence && fnew > SmallF && iterations < MaxIterations * xold.Count)
{
n = CalculateUpdate(freeValuesCount, xLength, originalData, cons, n, grad, deltaX);
////// line search + next steps /////
for (var i = 0; i < freeValuesCount; i++)
{
gradnew[i] = cons.Grad(originalData, i);
}
s = n * (-gradnew);
//copy newest values to the xold
xold = originalData;
f1 = fnew;
alphaStar = LineSearch(cons, xold, s, f1, alpha2, alpha1);
originalData = xold + alphaStar * s;
fnew = cons.Calc(originalData);
deltaX = originalData - xold;
grad = new Vector(gradnew);
deltaXnorm = deltaX.Norm();
iterations++;
}
// End of function
double validSolution = isFine < 0.1 ? ValidSolutionFine : ValidSoltuionRough;
if (fnew < validSolution)
{
return(0);
}
originalData = origSolution1;
return(1);
}