```/* nag_opt_bounds_qa_no_deriv (e04jcc) Example Program.
*
* Copyright 2014 Numerical Algorithms Group.
*
* Mark 23, 2011.
*
*/

#include <nag.h>
#include <math.h>
#include <stdio.h>
#include <string.h>
#include <nag_stdlib.h>
#include <nage04.h>
#include <nagx04.h>

#ifdef __cplusplus
extern "C" {
#endif
static void NAG_CALL objfun(Integer n, const double x[], double *f,
Nag_Comm *comm, Integer *inform);
static void NAG_CALL monfun(Integer n, Integer nf, const double x[], double f,
double rho, Nag_Comm *comm, Integer *inform);
#ifdef __cplusplus
}
#endif

int main(void)
{
static double ruser[2] = {-1.0, -1.0};
Integer       exit_status = 0;
double        rhobeg, rhoend, f;
Integer       i, n, nf, npt, maxcal;
double        *bl = 0, *bu = 0, *x = 0;
NagError      fail;
Nag_Comm    comm;

INIT_FAIL(fail);

printf("nag_opt_bounds_qa_no_deriv (e04jcc) Example Program Results\n");

/* For communication with user-supplied functions: */
comm.user = ruser;

maxcal = 500;
rhobeg = 1.0e-1;
rhoend = 1.0e-6;
n = 4;
npt = 2*n + 1;

if (!(x = NAG_ALLOC(n, double)) ||
!(bl = NAG_ALLOC(n, double)) ||
!(bu = NAG_ALLOC(n, double)))
{
printf("Allocation failure\n");
exit_status = -1;
goto END;
}

/* Set bounds on variables */
/* x[2] is not bounded, so we set bl[2] to a large negative
* number and bu[2] to a large positive number
*/
bl[0] = 1.0;
bl[1] = -2.0;
bl[2] = -1.0e10;
bl[3] = 1.0;
bu[0] = 3.0;
bu[1] = 0.0;
bu[2] = 1.0e10;
bu[3] = 3.0;
x[0] = 3.0;
x[1] = -1.0;
x[2] = 0.0;
x[3] = 1.0;

/* Call optimization routine */
/* nag_opt_bounds_qa_no_deriv (e04jcc).
Bound-constrained optimization by quadratic approximations. */
nag_opt_bounds_qa_no_deriv(objfun, n, npt, x, bl, bu, rhobeg, rhoend,
monfun, maxcal, &f, &nf, &comm, &fail);

if (fail.code == NE_NOERROR ||
fail.code == NE_TOO_MANY_FEVALS ||
fail.code == NE_TR_STEP_FAILED ||
fail.code == NE_RESCUE_FAILED ||
fail.code == NE_USER_STOP)
{

if (fail.code == NE_NOERROR)
{
printf("Successful exit.\n");
}

printf("Function value at lowest point found is %13.5f\n", f);
printf("The corresponding x is:");

for (i = 0; i <= n-1; ++i)
{
printf(" %13.5f", x[i]);
}

printf("\n");
}
else
{
exit_status = 1;
}

if (fail.code != NE_NOERROR)
{
printf("%s\n", fail.message);
}

END:
NAG_FREE(x);
NAG_FREE(bl);
NAG_FREE(bu);

return exit_status;
}

static void NAG_CALL objfun(Integer n, const double x[], double *f,
Nag_Comm *comm, Integer *inform)
{
/* Routine to evaluate objective function. */

double a, b, c, d, x1, x2, x3, x4;

if (comm->user[0] == -1.0)
{
printf("(User-supplied callback objfun, first invocation.)\n");
comm->user[0] = 0.0;
}
*inform = 0;
x1 = x[0];
x2 = x[1];
x3 = x[2];
x4 = x[3];

/* Supply a single function value */
a = x1 + 10.0*x2;
b = x3 - x4;
c = x2 - 2.0*x3, c *= c;
d = x1 - x4, d *= d;
*f = a*a + 5.0*b*b + c*c + 10.0*d*d;
}

static void NAG_CALL monfun(Integer n, Integer nf, const double x[], double f,
double rho, Nag_Comm *comm, Integer *inform)
{
/* Monitoring routine */
Integer j;

if (comm->user[1] == -1.0)
{
printf("(User-supplied callback monfun, first invocation.)\n");
comm->user[1] = 0.0;
}
*inform = 0;
printf("\nNew rho = %13.5f, number of function evaluations = %16"
NAG_IFMT "\n", rho, nf);
printf("Current function value = %13.5f\n", f);
printf("\nThe corresponding x is:\n");
for (j = 0; j <= n-1; ++j)
{
printf(" %13.5e", x[j]);
}
printf("\n");
}
```