a constraint has finite lower and upper bounds, OPT++ treats it as two separate constraints. In the computation of the residuals and gradients constraints with finite lower bounds appear first followed by those with finte upper bounds. Consequently, in the optimization summary, you will see the constraint count is double the original number of constraints.
Now, we are ready to build an constrained nonlinear program.
Let's consider the two-dimensional Rosenbrock problem with bound constraints.
minimize
subject to
Step 1: Build your compound constraint.
int ndim = 2; ColumnVector lower(ndim), upper(ndim); lower = -2.0; upper = 2.0; Constraint bc = new BoundConstraint(ndim, lower, upper); CompoundConstraint* rosen_constraints = new CompoundConstraint(bc);
Step 2: Create a nonlinear function with analytic derivatives.
void init_rosen (int ndim, ColumnVector& x) { if (ndim != 2) { exit (1); } x(1) = -1.2; x(2) = 1.0; }
void rosen(int mode, int n, const ColumnVector& x, double& fx, ColumnVector& g, int& result) { // Rosenbrock's function double f1, f2, x1, x2; if (n != 2) return; x1 = x(1); x2 = x(2); f1 = (x2 - x1 * x1); f2 = 1. - x1; if (mode & NLPFunction) { fx = 100.* f1*f1 + f2*f2; } if (mode & NLPGradient) { g(1) = -400.*f1*x1 - 2.*f2; g(2) = 200.*f1; } result = NLPFunction & NLPGradient; }
Step 3: Create a constrained nonlinear problem with analytic derivatives
NLF1 nips(n,rosen,init_rosen,rosen_constraints);
Voila! You're done.
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