NAG Library Manual, Mark 27.3
```/* nag_opt_handle_solve_bounds_foas (e04kfc) Example Program.
*
* Copyright 2021 Numerical Algorithms Group.
*
* Mark 27.3, 2021.
*/

/*
* NLP example: Nonlinear objective + box constraint
*/

#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 *fx,
Integer *inform, Nag_Comm *comm);
static void NAG_CALL objgrd(Integer nvar, const double x[], Integer nnzfd,
double fdx[], 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 *fx,
Integer *inform, Nag_Comm *comm) {
*fx = pow(1.0 - x[0], 2.0) + 100.0 * pow(x[1] - pow(x[0], 2.0), 2.0);
}

static void NAG_CALL objgrd(Integer nvar, const double x[], Integer nnzfd,
double fdx[], Integer *inform, Nag_Comm *comm) {
fdx[0] = 2.0 * x[0] - 400.0 * x[0] * (x[1] - pow(x[0], 2.0)) - 2.0;
fdx[1] = 200.0 * (x[1] - pow(x[0], 2.0));
}

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

int main(void) {
/* Define problem size */
#define NVAR 2

/* Scalars */
Integer nvar = NVAR;
Integer nu = 2 * nvar;

/* Arrays */
/* Lower bounds */
double blx[NVAR] = {-1.0, -2.0};
/* Upper bounds */
double bux[NVAR] = {0.8, 2.0};
/* Indexes for the gradient entries */
Integer idxfd[NVAR] = {1, 2};
/* Initial guess x0 */
double x[NVAR] = {-1.5, 1.9};
/* space holder for the Lagrange multiplyers */
double u[2 * NVAR];
double rinfo[100], stats[100];
void *handle = NULL;
char opt[80];

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

/* nag_file_open (x04acc).
*  Open unit number for reading, writing or appending, and
*  associate unit with named file
*/
nag_file_open("e04kf_cmon.txt", 1, &mon_out, NAGERR_DEFAULT);

/* nag_file_line_write (x04bac).
* Write formatted record to external file
*/
Vprintf("nag_opt_handle_solve_bounds_foas (e04kfc) "
"Example Program Results\n");
fflush(stdout);

/* nag_opt_handle_init (e04rac).
* Initialize an empty problem handle with NVAR variables.
*/
nag_opt_handle_init(&handle, nvar, NAGERR_DEFAULT);

/* nag_opt_handle_set_simplebounds (e04rhc).
* Define bounds on the variables
*/
nag_opt_handle_set_simplebounds(handle, nvar, blx, bux, NAGERR_DEFAULT);

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

/* nag_opt_handle_opt_set (e04zmc).
* Set optional arguments of the solver
*/
nag_opt_handle_opt_set(handle, "FOAS Print Frequency = 5", NAGERR_DEFAULT);

nag_opt_handle_opt_set(handle, "Print Solution = yes", NAGERR_DEFAULT);

sprintf(opt, "Monitoring File = %" NAG_IFMT, mon_out);
nag_opt_handle_opt_set(handle, opt, NAGERR_DEFAULT);

nag_opt_handle_opt_set(handle, "Monitoring Level = 3", NAGERR_DEFAULT);

nag_opt_handle_opt_set(handle, "Print Level = 1", NAGERR_DEFAULT);

/* Solver the problem
* nag_opt_handle_solve_bounds_foas (e04kfc).
*/
SET_FAIL(fail);
nag_opt_handle_solve_bounds_foas(handle, objfun, objgrd, monit, nvar, x,
rinfo, stats, &comm, &fail);

/* Print objective value at solution */
if (fail.code == NE_NOERROR || fail.code == NW_NOT_CONVERGED) {
Vprintf("\n\n  Solution found.\n"
"  Objective function value at solution: %8.1e\n",
rinfo[0]);
nag_opt_handle_set_get_real(handle, "Dual Variables", 1, &nu, u,
NAGERR_DEFAULT);
/* Print gradient vector FDX */
Vprintf("  Gradient at solution:                 %8.1e %8.1e\n\n",
u[0] - u[1], u[2] - u[3]);
/* Print Lagrange multipliers */
Vprintf("  Estimated Lagrange multipliers: blx   %8.1e %8.1e\n", u[0],
u[2]);
Vprintf("  Estimated Lagrange multipliers: bux   %8.1e %8.1e\n\n", u[1],
u[3]);
}

nag_file_close(mon_out, NAGERR_DEFAULT);

/* Clean up */
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 (0);
}
```