Optimization.ConjGrad Method (TRealFunction, TGrad, double[], [In] double[], [In] object[], out double, out TOptStopReason, [In] TMtxFloatPrecision, bool, bool, int, double, double, [In] TStrings)

Minimizes the function of several variables by using the Conjugate gradient optimization algorithm.

Syntax

Visual Basic

public static int ConjGrad(TRealFunction Fun, TGrad Grad, ref double[] Pars, [In] double[] Consts, [In] object[] ObjConst, out double FMin, out TOptStopReason StopReason, [In] TMtxFloatPrecision FloatPrecision, bool FletcherAlgo, bool SoftLineSearch, int MaxIter, double Tol, double GradTol, [In] TStrings Verbose);

Parameters

Parameters	Description
TRealFunction Fun	Real function (must be of TRealFunction type) to be minimized.
TGrad Grad	The gradient and Hessian procedure (must be of TGrad type), used for calculating the gradient.
ref double[] Pars	Stores the initial estimates for parameters (minimum estimate). After the call to routine returns adjusted calculated values (minimum position).
[In] double[] Consts	Additional Fun constant parameteres (can be/is usually nil).
[In] object[] ObjConst	Additional Fun constant parameteres (can be/is usually nil).
out double FMin	Returns function value at minimum.
out TOptStopReason StopReason	Returns reason why minimum search stopped (see TOptStopReason).
[In] TMtxFloatPrecision FloatPrecision	Specifies the floating point precision to be used by the routine.
bool FletcherAlgo	If True, ConjGrad procedure will use Fletcher-Reeves method. If false, ConjGrad procedure will use Polak-Ribiere method.
bool SoftLineSearch	If True, ConjGrad internal line search algoritm will use soft line search method. Set SoftLineSearch to true if you're using numerical approximation for gradient. If SoftLineSearch if false, ConjGrad internal line search algorithm will use exact line search method. Set SoftLineSearch to false if you're using exact gradient.
int MaxIter	Maximum allowed numer of minimum search iterations.
double Tol	Desired Pars - minimum position tolerance.
double GradTol	Minimum allowed gradient C-Norm.
[In] TStrings Verbose	If assigned, stores Fun, evaluated at each iteration step. Optionally, you can also pass TOptControl object to the Verbose parameter. This allows the optimization procedure to be interrupted from another thread and optionally also allows logging and iteration count monitoring.

Returns

the number of iterations required to reach the solution(minimum) within given tolerance.

Example

Problem: Find the minimum of the "Banana" function by using the Conjugate gradient method.

Solution:The Banana function is defined by the following equation:

Normally ConjGrad method would also require gradient procedure. But in this example we'll use the numerical approximation, more precisely the MtxIntDiff.NumericGradRichardson routine. This is done by specifying NumericGradRichardson routine as Grad parameter in ConjGrad routine call (see below)

// Objective function private double Banana(TVec x, TVec c, params object[] o) { return 100*Math387.IntPower(x[1] - Math387.IntPower(x[0],2),2) + Math387.IntPower(1-x[0],2); } private void Example() { double[2] Pars; double fmin; TOptStopReason StopReason; // initial estimates for x1 and x2 Pars[0] = 0; Pars[1] = 0; int iters = Optimization.ConjGrad(Banana, MtxIntDiff.NumericGradRichardson, Pars, null, null, out fmin, out StopReason, mvDouble, true, false, 1000, 1.0e-8, 1.0e-8, null); // stop if Iters >1000 or Tolerance < 1e-8 }

Group

ConjGrad Method

Links

Optimization Class, Optimization Members, Dew.Math.Units Namespace, ConjGrad Method, Example, See Also

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