NAG Library Manual, Mark 28.5
Interfaces:  FL   CL   CPP   AD
```/* nag_opt_handle_solve_dfno (e04jdc) Example Program.
*
* Copyright 2022 Numerical Algorithms Group.
*
* Mark 28.5, 2022.
*/

#include <math.h>
#include <nag.h>
#include <stdio.h>

#ifdef __cplusplus
extern "C" {
#endif
static void NAG_CALL objfun(Integer nvar, const double x[], double *f,
Integer *inform, Nag_Comm *comm);
static void NAG_CALL monit(Integer nvar, const double x[], Integer *inform,
const double rinfo[], const double stats[],
Nag_Comm *comm);
#ifdef __cplusplus
}
#endif

static void NAG_CALL objfun(Integer nvar, const double x[], double *f,
Integer *inform, Nag_Comm *comm) {
*f = pow(x[0] + 10.0 * x[1], 2) + 5.0 * pow(x[2] - x[3], 2) +
pow(x[1] - 2.0 * x[2], 4) + 10.0 * pow(x[0] - x[3], 4);
}

static void NAG_CALL monit(Integer nvar, const double x[], Integer *inform,
const double rinfo[], const double stats[],
Nag_Comm *comm) {}

int main(void) {
const double infbnd = 1.0e20;

Integer nvar, nnzfd;
Integer idxfd[4] = {1, 2, 3, 4};
double x[4] = {3.0, -1.0, 0.0, 1.0};
double rinfo[100], stats[100];
double ux[4] = {3.0, 0.0, infbnd, 3.0};
double lx[4] = {1.0, -2.0, -infbnd, 1.0};
void *handle;
Integer exit_status = 0;

/* Nag Types */
Nag_Comm comm;
NagError fail;

printf("nag_opt_handle_solve_dfno (e04jdc) Example Program Results\n\n");
fflush(stdout);

/* Fill the problem data structure */
nvar = 4;

/* nag_opt_handle_init (e04rac).
*  Initialize the handle
*/
nag_opt_handle_init(&handle, nvar, NAGERR_DEFAULT);

/* nag_opt_handle_set_nlnobj (e04rgc)
* Define nonlinear objective
*/
nnzfd = nvar;
nag_opt_handle_set_nlnobj(handle, nnzfd, idxfd, NAGERR_DEFAULT);

/* nag_opt_handle_opt_set (e04zmc)
* Set options
*/
/* Relax the main convergence criteria a bit */
nag_opt_handle_opt_set(handle, "DFO Trust Region Tolerance = 5.0e-6",
NAGERR_DEFAULT);
/* Print the solution */
nag_opt_handle_opt_set(handle, "Print Solution = YES", NAGERR_DEFAULT);
/* Set starting trust region (default was 0.1) */
nag_opt_handle_opt_set(handle, "DFO Starting trust Region = 0.2",
NAGERR_DEFAULT);

/* Define bounds for the variables
* nag_opt_handle_set_simplebounds (e04rhc)
*/
nag_opt_handle_set_simplebounds(handle, nvar, lx, ux, NAGERR_DEFAULT);

/* nag_opt_handle_solve_dfno (e04jdc)
* Call the solver
*/
INIT_FAIL(fail);
nag_opt_handle_solve_dfno(handle, objfun, monit, nvar, x, rinfo, stats, &comm,
&fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_opt_handle_solve_dfno (e04jdc).\n%s\n",
fail.message);
exit_status = 1;
}

/* Clean data */
if (handle)
/* nag_opt_handle_free (e04rzc).
* Destroy the problem handle and deallocate all the memory used
*/
nag_opt_handle_free(&handle, NAGERR_DEFAULT);

return exit_status;
}
```