public static Vector GradientDescent(IOptimizationFunction function, Vector x0, bool useGoldenRatio = true,
double epsilon = 10E-6)
{
var x = new DenseVector(x0.Count);
x0.CopyTo(x);
var iterations = 0;
var minimalLambda = -1.0;
for (var i = 0; i < MAX_ITERATIONS; i++)
{
double LambdaFunc(double lambda) =>
function.Function((Vector)(x + lambda * function.ComputeGradient(x)));
if (useGoldenRatio)
{
var golden = GoldenRatio(POINT, STEP, EPSILON, LambdaFunc);
minimalLambda = (golden.Left + golden.Right) / 2;
}
x = (DenseVector)(x + minimalLambda * function.ComputeGradient(x));
iterations = i;
if (function.ComputeGradient(x).L2Norm() < epsilon)
{
break;
}
}
Console.WriteLine($"Number of iterations: {iterations}");
return(x);
}
public static Vector Box(IOptimizationFunction function, Vector x0, List <Func <Vector, bool> > inequalities,
Vector lowerBounds, Vector upperBounds, int alpha = 2,
double epsilon = EPSILON)
{
var centroid = new DenseVector(x0.Count);
x0.CopyTo(centroid);
var iterations = 0;
var simplex = GenerateSimplex(x0, x0, lowerBounds, upperBounds, inequalities);
for (var j = 0; j < MAX_ITERATIONS; j++)
{
simplex = simplex.OrderByDescending(function.Function).ToList();
centroid = (DenseVector)GenerateCentroid(simplex);
var reflected = (Vector)((1 + alpha) * centroid - alpha * simplex[0]);
for (var i = 0; i < simplex.First().Count; i++)
{
reflected[i] = Math.Min(Math.Max(reflected[i], lowerBounds[i]), upperBounds[i]);
}
while (!CheckInequalitiesVector(reflected, inequalities))
{
reflected = (Vector)(0.5 * (reflected + centroid));
}
if (function.Function(reflected) > function.Function(simplex[1]))
{
reflected = (Vector)(0.5 * (reflected + centroid));
}
simplex[0] = reflected;
iterations = j;
if (CalculateStopCondition(simplex, centroid, function.Function) < epsilon)
{
break;
}
}
Console.WriteLine($"Number of iterations: {iterations}");
return(centroid);
}
