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New Version 7.0!  QuickStart Samples

# Linear Programming QuickStart Sample (C#)

Illustrates solving linear programming (LP) problems using classes in the Extreme.Mathematics.Optimization.LinearProgramming namespace in C#.

```using System;

namespace Extreme.Numerics.QuickStart.CSharp
{
// The linear programming classes reside in a namespace with
// other optimization-related classes.
using Extreme.Mathematics.Optimization;
// Vectors and matrices are in the Extreme.Mathematics
// namespace
using Extreme.Mathematics;

/// <summary>
/// Illustrates solving linear programming problems
/// using the classes in the Extreme.Mathematics.Optimization
/// namespace of the Extreme Optimization Numerical Libraries for .NET.
/// </summary>
class LinearProgramming
{
/// <summary>
/// The main entry point for the application.
/// </summary>
static void Main(string[] args)
{
// This QuickStart Sample illustrates the three ways to create a Linear Program.

// The first is in terms of matrices. The coefficients
// are supplied as a matrix. The cost vector, right-hand side
// and constraints on the variables are supplied as a vector.

// The cost vector:
var c = Vector.Create(-1.0, -3.0, 0.0, 0.0, 0.0, 0.0);
// The coefficients of the constraints:
var A = Matrix.Create(4, 6, new double[]
{
1, 1, 1, 0, 0, 0,
1, 1, 0, -1, 0, 0,
1, 0, 0, 0, 1, 0,
0, 1, 0, 0, 0, 1
}, MatrixElementOrder.RowMajor);
// The right-hand sides of the constraints:
var b = Vector.Create(1.5, 0.5, 1.0, 1.0);

// We're now ready to call the constructor.
// The last parameter specifies the number of equality
// constraints.
LinearProgram lp1 = new LinearProgram(c, A, b, 4);

// Now we can call the Solve method to run the Revised
// Simplex algorithm:
var x = lp1.Solve();
// The GetDualSolution method returns the dual solution:
var y = lp1.GetDualSolution();
Console.WriteLine("Primal: {0:F1}", x);
Console.WriteLine("Dual:   {0:F1}", y);
// The optimal value is returned by the Extremum property:
Console.WriteLine("Optimal value:   {0:F1}", lp1.OptimalValue);

// The second way to create a Linear Program is by constructing
LinearProgram lp2 = new LinearProgram();

// Next, we add two variables: we specify the name, the cost,
// and optionally the lower and upper bound.

// Next, we add constraints. Constraints also have a name.
// We also specify the coefficients of the variables,
// the lower bound and the upper bound.
// If a constraint is a simple equality or inequality constraint,
// you can supply a LinearProgramConstraintType value and the
// right-hand side of the constraint.

// We can now solve the linear program:
x = lp2.Solve();
y = lp2.GetDualSolution();
Console.WriteLine("Primal: {0:F1}", x);
Console.WriteLine("Dual:   {0:F1}", y);
Console.WriteLine("Optimal value:   {0:F1}", lp2.OptimalValue);

// Finally, we can create a linear program from an MPS file.
// The MPS format is a standard format.