How to: Use Unconstrained Non-Linear Programming

You can use the compact quasi-Newton solver (CompactQuasiNewtonSolver) for unconstrained non-linear programming. For example, you can find the global minimum of a two-dimensional Rosenbrock function created by mathematician Howard Rosenbrock in 1960.

To solve a 2-D Rosenbrock function

1. Create a Console Application named Rosenbrock.

2. Add a reference to Microsoft Solver Foundation on the .NET tab.

3. Add the following Imports or using statements to the top of the Program code file.

   using Microsoft.SolverFoundation.Common;
   using Microsoft.SolverFoundation.Solvers;
   

4. In the Main method, add a solver by typing the following:

   CompactQuasiNewtonSolver solver = new CompactQuasiNewtonSolver(2);
   

5. Set the delegate for getting the value and gradient at each point.

   solver.GradientAndValueAtPoint = TwoDimensionalRosenbrockFunction;
   

6. Solve the model and get the report.

   CompactQuasiNewtonSolutionQuality solutionQuality =
     solver.Solve(new CompactQuasiNewtonSolverParams());
   Console.Write(solver.ToString());
   

7. Define the TwoDimensionalRosenbrockFunction function outside of the Main method.

   private static double TwoDimensionalRosenbrockFunction(double[] point, double[] gradient) {
     double value = 
       (100 * Math.Pow(point[1] - Math.Pow(point[0], 2), 2)) +
       Math.Pow(1 - point[0], 2);
     gradient[0] = 
       400 * point[0] * (Math.Pow(point[0], 2) - point[1]) +
       2 * (point[0] - 1);
     gradient[1] = 200 * (point[1] - Math.Pow(point[0], 2));
     return value;
   }
   

8. Press F5 to build and run the code.

   The command window shows the following results.

   Minimize problem

   Dimensions = 2

   Starting point = 0, 0

   Solution quality is: LocalOptima

   Number of iterations performed: 21

   Finishing point =0.999999997671584, 0.999999995285991

   Finishing value =5.74844710320033E-18

See Also

Tasks

How to: Use Linear Programming using the Solver Foundation Services APIs

Concepts

Developing with Solver Foundation Services (SFS)