Nonlinear interior-point method with backtracking line-search

We use OptNIPS, which is a nonlinear interior-point algorithm that requires analytic Hessians, to solve problem 65 (hs65) from the Hock and Schittkowski suite of nonlinear programming problems. We limit the number of backtrack iterations to seven in the linesearch routine and use the residual of the first order optimality conditions as the merit function.

Moreover, we activate a method to restore infeasibility, if any, with respect to the inequality constraints in the problem formulation. We set the maximum number of iterations to five in the feasibility recovery method. The default number of iterations is three. Each iteration requires a constraint and constraint gradient evaluation.

```   #include <iostream>
#include <fstream>

#include "NLF.h"
#include "OptNIPS.h"
#include "hockfcns.h"

using NEWMAT::ColumnVector;

using namespace OPTPP;

void update_model(int, int, ColumnVector) {}

int main ()
{
int n = 3;

static char *status_file = {"tsthock65.out"};

//  Create a Constrained Nonlinear problem object
NLF2 nips(n,hs65,init_hs65,create_constraint_hs65);

//  Build a finite-difference NIPS object and optimize
OptNIPS objfcn(&nips, update_model);
objfcn.setOutputFile(status_file, 0);
objfcn.setFcnTol(1.0e-06);
objfcn.setMaxIter(150);
objfcn.setSearchStrategy(LineSearch);
objfcn.setMaxBacktrackIter(7);
objfcn.setMeritFcn(NormFmu);
objfcn.setFeasibilityRecovery(true);
objfcn.setMaxFeasIter(5);
objfcn.optimize();
objfcn.printStatus("Solution from nips");
objfcn.cleanup();

}
```

Last revised September 14, 2006 .