« Previous « Start » Next »

3  QP Problem

The general formulation in TOMNET for a quadratic programming problem is:

where c, x, x_L, x_U Rⁿ, F R^{n × n}, A R^{m₁ × n}, and b_L,b_U R^m₁. Equality constraints are defined by setting the lower bound equal to the upper bound, i.e. for constraint i: b_L(i) = b_U(i). Fixed variables are handled the same way.

Example problem:



The following code (maintained from the solution file: quickguide/qpQG/qpQG.sln) defines the problem in TOMNET.

using System;
using TOMNET;

namespace TOMNET
{
  /// <summary>
  /// Quick guide class for quadratic problem.
  /// </summary>
  static public class qpQG
  {
    /// <summary>
    /// Creates a simple quadratic problem.
    /// </summary>
    /// <returns>A simple quadratic problem.</returns>
    static public QuadraticProblem getQpQG()
    {
      //
      // Name of the problem.
      //
      string Name = "QP Example";

      //
      // Linear and quadratic part of the objective function
      // 1/2 * x' * F * x + c' * x
      //
      double[] F = new double[4] { 8, 1, 1, 8 };
      double[] c = new double[2] { 3, -4 };

      //
      // For use in bounds.
      //
      double Inf = double.PositiveInfinity;

      //
      // linear constraints and lower and upper bounds.
      //
      double[] A = new double[4] { 1, 1, 1, -1 };
      double[] b_L = new double[2] { -Inf, 0 };
      double[] b_U = new double[2] { 5, 0 };

      //
      // Lower and upper bounds for decision variables as well
      // as the starting point for the solver.
      //
      double[] x_L = new double[2] { 0, 0 };
      double[] x_U = new double[2] { Inf, Inf };
      double[] x_0 = new double[2] { 0, 1 };

      //
      // Create and return the quadratic problem
      //
      return QuadraticProblem.qpAssign(F, c, A, b_L, b_U, x_L, x_U, x_0,
        Name);
    }

    /// <summary>
    /// Testprogram for qpQG.
    /// </summary>
    static void Main()
    {
      //
      // Create a problem, solver and result instance.
      //
      QuadraticProblem Prob = qpQG.getQpQG();
      SNOPT solver = new SNOPT();
      Result result;

      //
      // Define a print file for SNOPT and a problem Name
      //
      Prob.Name += " (solved with SNOPT)";
      string printfilename = "SnoptQP.txt";
      solver.Options.PrintFile = printfilename;

      //
      // Solve the problem
      //
      solver.Solve(Prob, out result);

      //
      // Get the solution results
      //
      double[] solution = result.x_k;
      double objective = result.f_k;

      //
      // Display the solution on the console.
      //
      Console.WriteLine(" * * * * * * * *");
      Console.WriteLine(" * Solved a QP problem");
      Console.WriteLine(" * Printfile: " + printfilename);
      Console.WriteLine(" * Objective: {0}", objective);
      Console.WriteLine(" * Solution");
      Console.WriteLine("        x_L[i] <=     x_k[i] <=     x_U[i]");
      for (int i = 0; i < Prob.N; i++)
      {
        Console.WriteLine("    {0,10:g3} <= {1,10:g3} <= {2,10:g3} ",
          Prob.x_L[i], solution[i], Prob.x_U[i]);
      }

      double[] Ax = Prob.A.Evaluate(result.x_k);
      Console.WriteLine(" * Linear constraints");
      Console.WriteLine("        b_L[i] <=   (A*x)[i] <=     b_U[i]");
      for (int i = 0; i < Prob.mLin; i++)
      {
        Console.WriteLine("    {0,10:g3} <= {1,10:g3} <= {2,10:g3}",
          Prob.A.GetLowerBound(i), Ax[i], Prob.A.GetUpperBound(i));
      }
    }
  }
}

The solution file qpQG.sln  can be compiled to build an exe file. The executable can be run from the command prompt, which should display the following output results:

---

---

« Previous « Start » Next »