NAG Library Manual, Mark 30.1
```/* nag_opt_handle_solve_ssqp (e04src) Example Program.
*
* Copyright 2024 Numerical Algorithms Group.
*
* Mark 30.1, 2024.
*/

/* NLP example: Nonlinear objective, linear constraint and two nonlinear
* constraints.
*/

#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 *flag, Nag_Comm *comm);
static void NAG_CALL objgrd(Integer nvar, const double x[], Integer nnzfd,
double fdx[], Integer *flag, Nag_Comm *comm);
static void NAG_CALL confun(Integer nvar, const double x[], Integer ncnln,
double gx[], Integer *flag, Nag_Comm *comm);
static void NAG_CALL congrd(Integer nvar, const double x[], Integer nnzgd,
double gdx[], Integer *flag, Nag_Comm *comm);
#ifdef __cplusplus
}
#endif

int main(void) {
#define BIGBND 1.0E20
/* Scalars */
Integer exit_status = 0;
Integer i, idlc, nnzu, nvar, nclin, ncnln, nnzfd, nnzgd, flag;
double lmtest[4];

/* Arrays */
double rinfo[100], stats[100], *x = 0, *u = 0;
double *lambda = 0, *fdx = 0, *gdx = 0;
Integer idxfd[4] = {1, 2, 3, 4};
double bl[4] = {-BIGBND, -BIGBND, 0, 0};
double bu[4] = {BIGBND, BIGBND, BIGBND, BIGBND};
double linbl[1] = {0.0};
double linbu[1] = {BIGBND};
double nlnbl[2] = {2.0, 4.0};
double nlnbu[2] = {2.0, 4.0};
Integer irowb[2] = {1, 1};
Integer icolb[2] = {1, 2};
Integer irowgd[5] = {1, 1, 1, 2, 2};
Integer icolgd[5] = {1, 2, 3, 2, 4};
double b[2] = {2.0, 4.0};
Integer xlin[1] = {4};
void *handle = 0;

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

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

/* nag_file_line_write (x04bac).
* Write formatted record to external file
*/
nag_file_line_write(nout, "nag_opt_handle_solve_ssqp (e04src) "
"Example Program Results");

/* Problem size */
nvar = 4;
/* Counter for Lagrange multipliers */
nnzu = 0;
/* Objective gradient nonzero elements quantity */
nnzfd = 4;
/* Constraint jacobian nonzero elements quantity */
nnzgd = 5;

/* 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, bl, bu, NAGERR_DEFAULT);
/* Specify the amount of Lagrange mult. required */
nnzu += 2 * nvar;

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

/* Add one linear constraint */
nclin = 1;
idlc = 0;
/* nag_opt_handle_set_linconstr (e04rjc).
* Define a block of linear constraints
*/
nag_opt_handle_set_linconstr(handle, nclin, linbl, linbu, 2, irowb,
icolb, b, &idlc, NAGERR_DEFAULT);
/* Update the Lagrange mult. count */
nnzu += 2 * nclin;

/* Add two nonlinear constraints */
ncnln = 2;

/* nag_opt_handle_set_nlnconstr (e04rkc).
* Define a block of nonlinear constraints
*/
nag_opt_handle_set_nlnconstr(handle, ncnln, nlnbl, nlnbu, nnzgd, irowgd,
icolgd, NAGERR_DEFAULT);
/* Update the Lagrange mult. count */
nnzu += 2 * ncnln;

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

/* Define initial guess point */
for (i = 0; i < nvar; i++)
x[i] = i+1;

/* Optionally, define variable x(4) to be linear
* Hinting which variables are linear in problems with many
* variables can speed up performance
*/
nag_opt_handle_set_property(handle,"linear",1,xlin,NAGERR_DEFAULT);

/* Disable printing */
nag_opt_handle_opt_set(handle, "Print Level = 0", NAGERR_DEFAULT);
/* Do not print options */
nag_opt_handle_opt_set(handle, "Print Options = No", NAGERR_DEFAULT);
/* It is recommended on new problems to always verify the derivatives */
nag_opt_handle_opt_set(handle, "Verify Derivatives = Yes", NAGERR_DEFAULT);
/* Do not print solution, x and f(x) will be printed afterwards */
nag_opt_handle_opt_set(handle, "Print Solution = No", NAGERR_DEFAULT);

INIT_FAIL(fail);
/* nag_opt_handle_solve_ssqp (e04src).
* Call the solver
*/
nag_opt_handle_solve_ssqp(handle, objfun, objgrd, confun, congrd, NULLFN,
NULLFN, nvar, x, nnzu, u, rinfo, stats, &comm, &fail);
if (fail.code == NE_NOERROR) {
char msg[80];
nag_file_line_write(nout, "\nVariables");
for (i = 0; i < nvar; i++) {
sprintf(msg, "     x(%10" NAG_IFMT ")%17s=%16.2E", i + 1, "", x[i]);
nag_file_line_write(nout, msg);
}
nag_file_line_write(nout, "Variable bound Lagrange multipliers");
for (i = 0; i < nvar; i++) {
sprintf(msg, "    zL(%10" NAG_IFMT ")%17s=%16.2E", i + 1, "", u[2 * i]);
nag_file_line_write(nout, msg);
sprintf(msg, "    zU(%10" NAG_IFMT ")%17s=%16.2E", i + 1, "",
u[2 * i + 1]);
nag_file_line_write(nout, msg);
}
nag_file_line_write(nout, "Linear constraint Lagrange multipliers");
for (i = 0; i < nclin; i++) {
sprintf(msg, "    zL(%10" NAG_IFMT ")%17s=%16.2E", i + 1, "",
u[2 * nvar + 2 * i]);
nag_file_line_write(nout, msg);
sprintf(msg, "    zU(%10" NAG_IFMT ")%17s=%16.2E", i + 1, "",
u[2 * nvar + 2 * i + 1]);
nag_file_line_write(nout, msg);
}
nag_file_line_write(nout, "Nonlinear constraints Lagrange multipliers");
for (i = 0; i < ncnln; i++) {
sprintf(msg, "    zL(%10" NAG_IFMT ")%17s=%16.2E", i + 1, "",
u[2 * (nvar + nclin) + 2 * i]);
nag_file_line_write(nout, msg);
sprintf(msg, "    zU(%10" NAG_IFMT ")%17s=%16.2E", i + 1, "",
u[2 * (nvar + nclin) + 2 * i + 1]);
nag_file_line_write(nout, msg);
}

if (!(lambda = NAG_ALLOC((Integer)nnzu/2, double)) ||
!(fdx = NAG_ALLOC(nnzfd, double)) ||
!(gdx = NAG_ALLOC(nnzgd, double))) {
printf("Allocation failure\n");
exit_status = -1;
goto END;
}

/* Check of Lagrange multipliers (stationarity)
* Gradient of the objective (also available in data%coeffs(1:nnzfd))
*/
flag = 0;
objgrd(nvar, x, nnzfd, fdx, &flag, &comm);
if (flag != 0) {
exit_status = -1;
goto END;
}

/* Gradient of the nonlinear constraint */
flag = 0;
congrd(nvar, x, nnzgd, gdx, &flag, &comm);
if (flag != 0) {
exit_status = -1;
goto END;
}

/* Obtain the multipliers with correct sign
* 4 bound constraints, 1 linear constraint, and 2 nonlinear constraints
*/
for (i = 0; i < 7; i++) {
lambda[i] = u[2 * i + 1] - u[2 * i];
}
/* lambda (0..3) mult. related to bounds
* lambda (4) mult. related to linear constraints
* lambda (5..6) mult. related to the nonlinear constraint
*/
nag_file_line_write(nout, "Stationarity test for Lagrange multipliers");
lmtest[0] = fdx[0] + lambda[0] + lambda[4]*b[0] + lambda[5]*gdx[0];
lmtest[1] = fdx[1] + lambda[1] + lambda[4]*b[1] + lambda[5]*gdx[1]
+ lambda[6]*gdx[3];
lmtest[2] = fdx[2] + lambda[2] +                  lambda[5]*gdx[2];
lmtest[3] = fdx[3] + lambda[3]
+ lambda[6]*gdx[4];
for (i = 0; i < nvar; i++) {
if (lmtest[i] < 2.5e-8)
sprintf(msg, "    lx(%10" NAG_IFMT ")%17s=%16.2E%5s%6s", i + 1, "",
lmtest[i], "", "Ok    ");
else
sprintf(msg, "    lx(%10" NAG_IFMT ")%17s=%16.2E%5s%6s", i + 1, "",
lmtest[i], "", "Failed");
nag_file_line_write(nout, msg);
}

NAG_FREE(lambda);
NAG_FREE(fdx);
NAG_FREE(gdx);

sprintf(msg, "\nSolution found. Objective minimum  =%16.4E", rinfo[0]);
nag_file_line_write(nout, msg);
sprintf(msg, "             Constraint violation  =%6s%10.2E", "", rinfo[1]);
nag_file_line_write(nout, msg);
sprintf(msg, "             Dual infeasibility    =%6s%10.2E", "", rinfo[2]);
nag_file_line_write(nout, msg);
sprintf(msg, "   Iterations                      =     %11" NAG_IFMT,
(Integer) stats[0]);
nag_file_line_write(nout, msg);
sprintf(msg, "   Objective evaluations           =     %11" NAG_IFMT,
(Integer) stats[18]);
nag_file_line_write(nout, msg);
sprintf(msg, "   Objective gradient evaluations  =     %11" NAG_IFMT,
(Integer) stats[4]);
nag_file_line_write(nout, msg);
sprintf(msg, "   Constraint evaluations          =     %11" NAG_IFMT,
(Integer) stats[19]);
nag_file_line_write(nout, msg);
sprintf(msg, "   Constraint gradient evaluations =     %11" NAG_IFMT,
(Integer) stats[20]);
nag_file_line_write(nout, msg);
sprintf(msg, "   Hessian evaluations             =     %11" NAG_IFMT,
(Integer) stats[3]);
nag_file_line_write(nout, msg);
} else {
printf("Error from nag_opt_handle_solve_ssqp (e04src).\n%s\n",
fail.message);
exit_status = 1;
}
if (handle)
/* nag_opt_handle_free (e04rzc).
* Destroy the problem handle and deallocate all the memory used
*/
nag_opt_handle_free(&handle, NAGERR_DEFAULT);

NAG_FREE(x);
NAG_FREE(u);

END:
return exit_status;
}

/* Subroutines */
static void NAG_CALL objfun(Integer nvar, const double x[], double *fx,
Integer *flag, Nag_Comm *comm) {
*fx = (x[0]+x[1]+x[2])*(x[0]+x[1]+x[2]) + 3.0*x[2] + 5.0*x[3] + cos(0.01*x[0]) - 1.0;

*flag = 0;
}
static void NAG_CALL objgrd(Integer nvar, const double x[], Integer nnzfd,
double fdx[], Integer *flag, Nag_Comm *comm) {
double sum;
sum = 2.0*(x[0]+x[1]+x[2]);

fdx[0] = sum - 0.01*sin(0.01*x[0]);
fdx[1] = sum;
fdx[2] = sum + 3.0;
fdx[3] = 5.0;

*flag = 0;
}
static void NAG_CALL confun(Integer nvar, const double x[], Integer ncnln,
double gx[], Integer *flag, Nag_Comm *comm) {
gx[0] = x[0]*x[0] + x[1]*x[1] + x[2];
gx[1] = x[1]*x[1]*x[1]*x[1] + x[3];

*flag = 0;
}
static void NAG_CALL congrd(Integer nvar, const double x[], Integer nnzgd,
double gdx[], Integer *flag, Nag_Comm *comm) {
gdx[0] = 2.0*x[0];
gdx[1] = 2.0*x[1];
gdx[2] = 1.0;
gdx[3] = 4.0*x[1]*x[1]*x[1];
gdx[4] = 1.0;

*flag = 0;
}
```