nonlinear optimization using the Solver Foundation Services

Question

I have a non-linear optimization problem with constraints. It can be solved in Microsoft Excel with the Solver add-in, but I am having trouble replicating that in C#.

I installed the Microsoft Solver Foundation dll

This is the example where I adapted my code from : http://msdn.microsoft.com/en-us/library/gg261758(v=vs.93).aspx?cs-save-lang=1&cs-lang=csharp#code-snippet-3

Basically, in my code, I have 2 parameters called RHO and NU. I need to get their optimal values which minimizes the sum of squares. I have ONLY 1 value for RHO and 1 value for NU, so I know that putting RHO[s] and NU[s] in my code is wrong, but when I replace them with RHO and NU, I get errors.

Another issue is that, in the example, the code looks for one optimal variable called "fuel" of type "Goal". In my case, I have 2 variables which need to be optimized.

Obviously, the program breaks at the last line, it says: "there is no solution to propagate".

Anyone has an idea how my code could be corrected ?? any help is appreciated !

This is my code:

    class Segment
    {
        public double Strike { get; set; }
        public double VolImp { get; set; }
        public double _Rho_ { get; set; }
        public double _Nu_ { get; set; }
        public double _Alpha_ { get; set; }
    }



       Segment[] segmentData = new Segment[] { 
            new Segment { Strike = 5, VolImp = 53.2608},
            new Segment { Strike = 10, VolImp = 48.3773},
            new Segment { Strike = 20, VolImp = 43.8949},
            new Segment { Strike = 30, VolImp = 40.9367},
            new Segment { Strike = 40, VolImp = 38.891},
            new Segment { Strike = 50, VolImp = 37.417},
            new Segment { Strike = 60, VolImp = 36.2838},
            new Segment { Strike = 70, VolImp = 35.3713},
            new Segment { Strike = 80, VolImp = 34.6192},
            new Segment { Strike = 90, VolImp = 33.9774},
            new Segment { Strike = 100, VolImp = 33.4359},
            new Segment { Strike = 110, VolImp = 32.9747},
            new Segment { Strike = 120, VolImp = 32.5635},
            new Segment { Strike = 130, VolImp = 32.2025},
            new Segment { Strike = 140, VolImp = 31.8917},
            new Segment { Strike = 150, VolImp = 31.6209},
            new Segment { Strike = 160, VolImp = 31.3702},
            new Segment { Strike = 170, VolImp = 31.1596},
            new Segment { Strike = 180, VolImp = 30.9591},
       };


        SolverContext context = SolverContext.GetContext();
        Model model = context.CreateModel();



        // Parameters
        Set segments = new Set(Domain.Integer, "segments");

        Parameter RHO = new Parameter(Domain.Real, "RHO", segments);
        RHO.SetBinding(segmentData, "_Rho_", "Strike");

        Parameter NU = new Parameter(Domain.RealNonnegative, "NU", segments);
        NU.SetBinding(segmentData, "_Nu_", "Strike");

        Parameter ALPHA = new Parameter(Domain.RealNonnegative, "ALPHA", segments);
        ALPHA.SetBinding(segmentData, "_Alpha_", "Strike");

        Parameter MyStrike = new Parameter(Domain.RealNonnegative, "MyStrike", segments);
        MyStrike.SetBinding(segmentData, "Strike", "Strike");

        Parameter MyImpVol = new Parameter(Domain.RealNonnegative, "MyImpVol", segments);
        MyImpVol.SetBinding(segmentData, "VolImp", "Strike");

        model.AddParameters(RHO, NU, ALPHA, MyStrike, MyImpVol);


        //Constraints
        model.AddConstraint("rho_bound", Model.ForEach(segments, s => (-1 <= RHO[s] <= 1))) ;
        model.AddConstraint("nu_bound", Model.ForEach(segments, s => (0 <= NU[s]) )) ;
        model.AddConstraint("alpha_bound", Model.ForEach(segments, s => (0 < ALPHA[s]))) ;

        double Forward = 100 ;

        //Goal
        Goal Mygoal = model.AddGoal("Mygoal", GoalKind.Minimize, Model.Sum(Model.ForEach(segments, s => Model.Power((MyImpVol[s] - (ALPHA[s] * (NU[s] / ALPHA[s] * Model.Log(Forward / MyStrike[s])) * (Model.Log((Model.Sqrt(1 - 2 * RHO[s] * (NU[s] / ALPHA[s] * Model.Log(Forward / MyStrike[s])) + Model.Power((NU[s] / ALPHA[s] * Model.Log(Forward / MyStrike[s])), 2)) + (NU[s] / ALPHA[s] * Model.Log(Forward / MyStrike[s])) - RHO[s]) / (1 - RHO[s]))) * (1 + (0.25 * RHO[s] * NU[s] * ALPHA[s] + (2 - 3 * RHO[s] * RHO[s]) / 24 * NU[s] * NU[s]) * 6.46407))), 2)))) ;


        //solve
        context.Solve();
        context.PropagateDecisions();