Help with OPT++ constraints

kwoodle · 3/22/10

I am using open source (Sandia Labs) OPT++ with newmat to model a GARCH(1,1) process. I need to estimate the parameters (omega, alpha, beta) which give the maximum likelihood. I have convinced myself that the likelihood function is correct. When I minimize (the negative) of the likelihood function without constraints it quickly goes to minus infinity as expected. I wish to implement the constraints

C++:

0 < omega
0 < alpha + beta < 1

This requires modification

C++:

eps = 1.e-6
eps < omega < 1./eps
eps < alpha + beta < 1. - eps

OPT++ has the capability to represent a constraint

C++:

    double eps = 1.0e-6;
    Matrix A(2,3);
    A << 0. << 1. << 1.
      << 1. << 0. << 0.;
    ColumnVector lower(2);
    lower << eps << eps;
    ColumnVector upper(2);
    double upp1 = 1.0 - eps;
    double upp2 = 1.0/eps;
    upper << upp1 << upp2;
    Constraint ineq = new LinearInequality(A, lower, upper);
    CompoundConstraint cc(ineq);
    
    // Nonlinear likelihood function
    // with 3 params, and (linear? constraint)
    NLF0 nlp(ndim, like, init_like, &cc);

    // The search algorithm used in minimization of -likelihood
    OptPDS objfcn(&nlp);
.
.
 .
 try {
  objfcn.optimize();
  }
   // catch exceptions thrown by newmat
   catch(BaseException) { cout << BaseException::what() << endl; }

   catch(...) { cout << "exception caught in main program" << endl; }

The code throws the exception

C++:

An exception has been thrown
Logic error:- detected by Newmat: index error: requested index = 3

MatrixType = Rect   # Rows = 2; # Cols = 1

It seems (from looking in the debugger) that a simplex search is being
set up and it's checking whether lower bounds are lower that upper bounds.
I suspect its a long shot that anyone has experienced this particular problem,
but I'm stuck trying to figure this out
Thanks and Cheers
K

Springer · 3/23/10

I coded up a garch class in C# not too long ago that used either a Simplex or a heuristic search method, unfortunately I'm unfamiliar with OPT++.

But if it helps here is my negative log likelihood (no mean eq):

C++:

//NEGATIVE LOG LIKELIHOOD FUNCTION
        static public double F(double[] theta)
        {
            int n = LnReturns.Length;
            double LLsum = 0;

            for (int i = 1; i < n; ++i)
            {
                sigma2[i] = theta[2] + theta[0] * sigma2[i - 1] +
                            theta[1] * LnReturns[i - 1] * LnReturns[i - 1];
            }

            for (int i = 1; i < n; ++i)
            {
                LL[i] = 0.5 * Math.Log(2 * Math.PI) -
                            0.5 * ((LnReturns[i] * LnReturns[i]) / sigma2[i]) -
                            0.5 * Math.Log(sigma2[i]);

                LLsum += LL[i];
            }

            return -LLsum;
        }

and for the simplex I had to do some fiddling but found this,

C++:

double[,] simplex = {   {0.65, 0.02, 0.00001}, 
                                        {0.85, 0.08, 0.00001},
                                        {0.95, 0.10, 0.00001},
                                        {0.70, 0.20, 0.00002}   };
                Param = Solve.minimize(F, simplex);

worked well.

Hope that is at least of some use

Help with OPT++ constraints

kwoodle

Springer