# C# Interior Point QP Example

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```ï»¿using System;

using CenterSpace.NMath.Core;
using CenterSpace.NMath.Analysis;

namespace CenterSpace.NMath.Analysis.Examples.CSharp
{
/// <summary>
/// A .NET example in C# showing how to use the interior point quadratic
/// programming solver <c>InteriorPointQPSolver</c> to solve a quadratic
/// programming problem.
/// </summary>
public class InteriorPointQPExample
{
static void Main( string[] args )
{
// Use the InteriorPointQPSolver class to solve a quadratic programming
// problem of the form
// 0.5*x'Hx + x'c
// Our problem will have 4 variables and eight constraints. In addition
// the variables will be required to be nonnegative.

// Construct the 4x4 H matrix and c vector for the problem.
var HMatrixData = new double[,] { {3.0625,  0.0000,  0.0000, 0.0000},
{ 0.0000, 0.0405,  0.0000, 0.0000},
{ 0.0000,  0.0000, 0.0271, -0.0031},
{ 0.0000,  0.0000,  -0.0031, 0.0054} };
var H = new DoubleMatrix( HMatrixData );
var c = new DoubleVector( -2671.0, -135.0, -103.0, -19.0 );

// Construct the quadratic programming problem from H and c.
var problem = new QuadraticProgrammingProblem( H, c );

// Our problem will have 8 linear constraints and will be of the form
// Cx <= b
// Where C is an 8x4 matrix and b is a vector of length 8.

// Construct the C matrix and b vector.
var CmatrixData = new double[,]
{
{-0.0401, -0.0162, -0.0039, 0.0002},
{-0.1326, -0.0004, -0.0034, 0.0006},
{1.5413, 0.0, 0.0, 0.0 },
{0.0, 0.0203, 0.0, 0.0},
{0.0, 0.0, 0.0136, -0.0075},
{0.0, 0.0, -0.0016, 0.0027},
{0.0160, 0.0004, 0.0005, 0.0002}
};
var C = new DoubleMatrix( CmatrixData );
var b = new DoubleVector( -92.6, -29.0, 2671.0, 135.0, 103.0, 19.0, 10.0 );

// Now, add the constraints to the problem.
for ( int i = 0; i < C.Rows; i++ )
{
problem.AddUpperBoundConstraint( C.Row( i ), b[i] );
}

// Add variable bounds. Variable values are required to be >= 0.
for ( int i = 0; i < 4; i++ )
{
}

// Construct the solver.
var solver = new InteriorPointQPSolver();

// Set parameters for the solve.
var solverParams = new InteriorPointQPSolverParams
{
KktForm = InteriorPointQPSolverParams.KktFormOption.Blended,
Tolerance = 1e-6,
MaxDenseColumnRatio = 0.9,
PresolveLevel = InteriorPointQPSolverParams.PresolveLevelOption.Full,
SymbolicOrdering = InteriorPointQPSolverParams.SymbolicOrderingOption.ApproximateMinDegree
};

solver.Solve( problem, solverParams );
Console.WriteLine( "\nSolver Parameters:" );
Console.WriteLine( solverParams.ToString() );
Console.WriteLine( "\nResult = " + solver.Result );
Console.WriteLine( "Optimal x = " + NMathFunctions.Round( solver.OptimalX, 0 ) );
Console.WriteLine( "Optimal Function value = " + solver.OptimalObjectiveFunctionValue.ToString( "F3" ) );
Console.WriteLine( "iterations = " + solver.IterationCount );

Console.WriteLine();
Console.WriteLine( "Press Enter Key" );