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system 10.5 of 29/11/2024,
©
FORESIGHT
LagrangeMultiplier: Double;
The LagrangeMultiplier property determines value of Lagrange multiplier.
Lagrange multiplier determines the degree, to which constraint value is close to its border.
To execute the example, add a link to the Stat system assembly.
Sub UserProc;
Var
i, N, Res: Integer;
d, OptVal: Double;
CF, Lb, Ub, LagrMultEtalon1, LagrMultEtalon2: Array Of Double;
LinC1, LinC2, LinC3, LinC4, LinC5, LinC6, LinC7: ISlLinearConstraint;
LP: SmLinearProgramming;
Bound: ISlBoundaryRegion;
LC1, LC2, LC3, LC4, LC5, LC6, LC7, Sol, LPBL, LPBU, LPLM: Array Of Double;
inft: Double;
LCon1: ISlLinearConstraint;
Begin
LP := New SmLinearProgramming.Create;
LP.InitialApproximation.AutoCreate := True;
N := 7;
inft := double.PositiveInfinity;
CF := New Double[N];
Lb := New Double[N];
Ub := New Double[N];
LC1 := New Double[N];
LC2 := New Double[N];
LC3 := New Double[N];
LC4 := New Double[N];
LC5 := New Double[N];
LC6 := New Double[N];
LC7 := New Double[N];
LagrMultEtalon1 := New double[N];
LagrMultEtalon2 := New double[7];
// Multipliers for common constraints
LagrMultEtalon1[0] := 0.3301;
LagrMultEtalon1[1] := 0.01438;
LagrMultEtalon1[2] := -0.09100;
LagrMultEtalon1[3] := -0.07661;
LagrMultEtalon1[4] := 0;
LagrMultEtalon1[5] := 0;
LagrMultEtalon1[6] := 0;
// Multipliers for linear constraints
LagrMultEtalon2[0] := -1.431;
LagrMultEtalon2[1] := 0;
LagrMultEtalon2[2] := 0;
LagrMultEtalon2[3] := 0;
LagrMultEtalon2[4] := 0;
LagrMultEtalon2[5] := 1.501;
LagrMultEtalon2[6] := 1.517;
// Values
cf[0] := -0.02; cf[1] := -0.2; cf[2] := -0.2; cf[3] := -0.2; cf[4] := -0.2; cf[5] := 0.04; cf[6] := 0.04;
ub[0] := 0.01; ub[1] := 0.15; ub[2] := 0.03; ub[3] := 0.02; ub[4] := 0.05; ub[5] := 1e20; ub[6] := 1e20;
lb[0] := -0.01; lb[1] := -0.1; lb[2] := -0.01; lb[3] := -0.04; lb[4] := -0.1; lb[5] := -0.01; lb[6] := -0.01;
lc1[0] := 1; lc1[1] := 1; lc1[2] := 1; lc1[3] := 1; lc1[4] := 1; lc1[5] := 1; lc1[6] := 1;
lc2[0] := 0.15; lc2[1] := 0.04; lc2[2] := 0.02; lc2[3] := 0.04; lc2[4] := 0.02; lc2[5] := 0.01; lc2[6] := 0.03;
lc3[0] := 0.03; lc3[1] := 0.05; lc3[2] := 0.08; lc3[3] := 0.02; lc3[4] := 0.06; lc3[5] := 0.01; lc3[6] := 0;
lc4[0] := 0.02; lc4[1] := 0.04; lc4[2] := 0.01; lc4[3] := 0.02; lc4[4] := 0.02; lc4[5] := 0; lc4[6] := 0;
lc5[0] := 0.02; lc5[1] := 0.03; lc5[2] := 0; lc5[3] := 0; lc5[4] := 0.01; lc5[5] := 0; lc5[6] := 0;
lc6[0] := 0.70; lc6[1] := 0.75; lc6[2] := 0.8; lc6[3] := 0.75; lc6[4] := 0.8; lc6[5] := 0.97; lc6[6] := 0;
lc7[0] := 0.02; lc7[1] := 0.06; lc7[2] := 0.08; lc7[3] := 0.12; lc7[4] := 0.02; lc7[5] := 0.01; lc7[6] := 0.97;
// Criterion function
LP.CriterionFunction := CF;
// Area borders
Bound := LP.Boundary;
// Area lower boundary
Bound.BoundaryLower := Lb;
// Upper area boundary
Bound.BoundaryUpper := Ub;
// First coefficient of linear constraint
LinC1 := LP.LinearConstraints.Add;
LinC1.Value := LC1;
// Lower linear constraint
LinC1.BoundaryLower := -0.13;
// Upper boundary constraint
LinC1.BoundaryUpper := -0.13;
// Second coefficient of linear constraint
LinC2 := LP.LinearConstraints.Add;
LinC2.Value := LC2;
// Lower linear constraint
LinC2.BoundaryLower := -inft;
// Upper linear constraint
LinC2.BoundaryUpper := -0.0049;
// Third coefficient of linear constraint
LinC3 := LP.LinearConstraints.Add;
LinC3.Value := LC3;
// Lower linear constraint
LinC3.BoundaryLower := -inft;
// Upper linear constraint
LinC3.BoundaryUpper := -0.0064;
// Fourth linear constraint coefficient
LinC4 := LP.LinearConstraints.Add;
LinC4.Value := LC4;
// Lower linear constraint
LinC4.BoundaryLower := -inft;
// Upper linear constraint
LinC4.BoundaryUpper := -0.0037;
// Fifth linear constraint coefficient
LinC5 := LP.LinearConstraints.Add;
LinC5.Value := LC5;
// Lower linear constraint
LinC5.BoundaryLower := -inft;
// Upper linear constraint
LinC5.BoundaryUpper := -0.0012;
// Sixth linear constraint coefficient
LinC6 := LP.LinearConstraints.Add;
LinC6.Value := LC6;
// Lower linear constraint
LinC6.BoundaryLower := -0.0992;
// Upper linear constraint
LinC6.BoundaryUpper := inft;
// Seventh linear constraint coefficient
LinC7 := LP.LinearConstraints.Add;
LinC7.Value := LC7;
// Lower linear constraint
LinC7.BoundaryLower := -0.003;
// Upper linear constraint
LinC7.BoundaryUpper := 0.002;
// Model calculation
Res := LP.Execute;
// Any errors
Debug.WriteLine("Execution status: " + LP.Errors);
Debug.WriteLine("== Criterion function value ==");
OptVal := LP.OptimalFunctionValue;
Debug.WriteLine(OptVal.ToString);
Debug.WriteLine("== Solution ==");
Sol := LP.Solution;
For i := 0 To N - 1 Do
d := Sol[i];
Debug.WriteLine(i.ToString + ": " + d.ToString);
End For;
Debug.WriteLine("== Common constraints: ==");
d := 0;
LPBL := Bound.BoundaryLower;
LPBU := Bound.BoundaryUpper;
LPLM := Bound.LagrangeMultiplier;
For i := 0 To N - 1 Do
d := LP.Solution[i];
Debug.WriteLine(i.ToString + ": ");
Debug.WriteLine(LPBL[i].ToString + "<=" + d.ToString + "<= " + LPBU[i].ToString);
Debug.WriteLine("Lagrange multiplier: " + LPLM[i].ToString);
Debug.WriteLine("Reference Lagrange multiplier: " + LagrMultEtalon1[i].ToString);
Debug.WriteLine(" ");
End For;
Debug.WriteLine(" ");
Debug.WriteLine("== Linear constraints ==");
For i := 0 To LP.LinearConstraints.Count - 1 Do
LCon1 := LP.LinearConstraints.Item(i);
Debug.WriteLine(i.ToString + ": " + LCon1.BoundaryLower.ToString + " <= " + LCon1.Result.ToString + " <= " + LCon1.BoundaryUpper.ToString);
Debug.WriteLine("Lagrange multiplier: " + LCon1.LagrangeMultiplier.ToString);
Debug.WriteLine("Reference Lagrange multiplier: " + LagrMultEtalon2[i].ToString);
Debug.WriteLine(" ");
End For;
End Sub UserProc;
After executing the example the console window displays:
If there are any calculation errors.
Criterion function value
Model calculation results: common and general constraints and Lagrange multipliers.
See also: