NAG Library Manual, Mark 28.3
```/* E04UE_P0W_F C++ Header Example Program.
*
* Copyright 2022 Numerical Algorithms Group.
* Mark 28.3, 2022.
*/

#include <iostream>
#include <math.h>
#include <nag.h>
#include <stdio.h>
#include <string>
using namespace std;

int main()
{
// Scalars
int exit_status = 0;

cout << "E04UE_P0W_F C++ Header Example Program Results\n\n";

Integer           ifail = 0;

// Skip first line of data file
string mystr;
getline(cin, mystr);

Integer n, nclin, ncnln;
cin >> n;
cin >> nclin;
cin >> ncnln;

Integer liwork = 3 * n + nclin + 2 * ncnln;
Integer lda = nclin, sda = n, ldcj = ncnln, ldr = n;
Integer lwork;

lwork = 20 * n;
if (nclin > 0 || ncnln > 0)
{
lwork = lwork + 2 * n * n;
if (nclin > 0)
{
lwork = lwork + 11 * nclin;
;
}
if (ncnln > 0)
{
lwork = lwork + n * nclin + 2 * n * ncnln + 21 * ncnln;
}
}
if (ncnln > 0)
{
lwork = lwork + n * nclin + (2 * n + 21) * ncnln;
}
Integer  lb = n + nclin + ncnln;
double * a = 0, *bl = 0, *bu = 0, *c = 0, *cjac = 0;
double * objgrd = 0, *clamda = 0, *r = 0, *x = 0, *work = 0, *rwsav = 0;
Integer *istate = 0, *iwork = 0, *iwsav = 0;
logical *lwsav = 0;
a              = new double[lda * sda];
bl             = new double[lb];
bu             = new double[lb];
c              = new double[ncnln];
cjac           = new double[ncnln * n];
clamda         = new double[lb];
r              = new double[ldr * n];
x              = new double[n];
objgrd         = new double[n];
work           = new double[lwork];
rwsav          = new double[475];
lwsav          = new logical[120];
istate         = new Integer[lb];
iwork          = new Integer[liwork];
iwsav          = new Integer[610];

// Read problem parameters and register for differentiation
for (int i = 0; i < nclin; i++)
{
for (int j = 0; j < sda; j++)
{
Integer k = i + j * nclin;
cin >> a[k];
}
}
for (int i = 0; i < lb; i++)
{
cin >> bl[i];
}
for (int i = 0; i < lb; i++)
{
cin >> bu[i];
}
for (int i = 0; i < n; i++)
{
cin >> x[i];
}
double ruser[3];
for (int i = 0; i < 3; i++)
{
ruser[i] = 1.0;
}

// Initialize sav arrays
ifail = 0;
char cwsav[1];
nag::ad::e04wb("E04UCA", cwsav, 1, lwsav, 120, iwsav, 610, rwsav, 475, ifail);

Integer &               mode,
const Integer &         n,
const double *x,
double &     objf,
double *objgrd,
const Integer &         nstate)
{
if (mode == 0 || mode == 2)
{
objf = x[0] * x[3] * (ruser[0] * x[0] + ruser[1] * x[1] + ruser[2] * x[2]) +
x[2];
}
if (mode == 1 || mode == 2)
{
objgrd[0] =
x[3] * (2.0 * ruser[0] * x[0] + ruser[1] * x[1] + ruser[2] * x[2]);
objgrd[1] = x[0] * x[3] * ruser[1];
objgrd[2] = x[0] * x[3] * ruser[2] + 1.0;
objgrd[3] = x[0] * (ruser[0] * x[0] + ruser[1] * x[1] + ruser[2] * x[2]);
}
};
Integer &               mode,
const Integer &         ncnln,
const Integer &         n,
const Integer &         ldcj,
const Integer           needc[],
const double *x,
double *c,
double *cjac,
const Integer &         nstate)
{
if (nstate == 1)
{
for (int i = 0; i < ncnln * n; ++i)
{
cjac[i] = 0.0;
}
}
if (needc[0] > 0)
{
if (mode == 0 || mode == 2)
{
c[0] = x[0] * x[0] + x[1] * x[1] + x[2] * x[2] + x[3] * x[3];
}
if (mode == 1 || mode == 2)
{
cjac[0]         = x[0] + x[0];
cjac[ncnln]     = x[1] + x[1];
cjac[2 * ncnln] = x[2] + x[2];
cjac[3 * ncnln] = x[3] + x[3];
}
}
if (needc[1] > 0)
{
if (mode == 0 || mode == 2)
{
c[1] = x[0] * x[1] * x[2] * x[3];
}
if (mode == 1 || mode == 2)
{
cjac[1]             = x[1] * x[2] * x[3];
cjac[ncnln + 1]     = x[0] * x[2] * x[3];
cjac[2 * ncnln + 1] = x[0] * x[1] * x[3];
cjac[3 * ncnln + 1] = x[0] * x[1] * x[2];
}
}
};

// Solve the problem
Integer iter;
double  objf;
ifail = -1;
objfun, iter, istate, c, cjac, clamda, objf, objgrd, r, x,
iwork, liwork, work, lwork, lwsav, iwsav, rwsav, ifail);

// Primal results
cout.setf(ios::scientific, ios::floatfield);
if (ifail == 0 || ifail > 1)
{
cout.precision(4);
cout << "\n Optimal objective function value = ";
cout.width(12);
cout << objf;
cout << "\n Solution point = ";
for (int i = 0; i < n; i++)
{
cout.width(12);
cout << x[i];
}
cout << endl;
}
else
{
cout << "nag::ad::e04uc failed with ifail = " << ifail << endl;
}

delete[] a;
delete[] bl;
delete[] bu;
delete[] c;
delete[] cjac;
delete[] clamda;
delete[] r;
delete[] x;
delete[] objgrd;
delete[] work;
delete[] rwsav;
delete[] lwsav;
delete[] istate;
delete[] iwork;
delete[] iwsav;
return exit_status;
}

Integer &          mode,
const Integer &    n,
const double       x[],
double &           objf,
double             objgrd[],
const Integer &    nstate,
Integer            iuser[],
double             ruser[])
{
if (mode == 0 || mode == 2)
{
objf = x[0] * x[3] * (ruser[0] * x[0] + ruser[1] * x[1] + ruser[2] * x[2]) +
x[2];
}
if (mode == 1 || mode == 2)
{
objgrd[0] =
x[3] * (2.0 * ruser[0] * x[0] + ruser[1] * x[1] + ruser[2] * x[2]);
objgrd[1] = x[0] * x[3] * ruser[1];
objgrd[2] = x[0] * x[3] * ruser[2] + 1.0;
objgrd[3] = x[0] * (ruser[0] * x[0] + ruser[1] * x[1] + ruser[2] * x[2]);
}
return;
}
Integer &          mode,
const Integer &    ncnln,
const Integer &    n,
const Integer &    ldcj,
const Integer      needc[],
const double       x[],
double             c[],
double             cjac[],
const Integer &    nstate,
Integer            iuser[],
double             ruser[])
{
if (nstate == 1)
{
for (int i = 0; i < ncnln * n; ++i)
{
cjac[i] = 0.0;
}
}
if (needc[0] > 0)
{
if (mode == 0 || mode == 2)
{
c[0] = x[0] * x[0] + x[1] * x[1] + x[2] * x[2] + x[3] * x[3];
}
if (mode == 1 || mode == 2)
{
cjac[0]         = x[0] + x[0];
cjac[ncnln]     = x[1] + x[1];
cjac[2 * ncnln] = x[2] + x[2];
cjac[3 * ncnln] = x[3] + x[3];
}
}
if (needc[1] > 0)
{
if (mode == 0 || mode == 2)
{
c[1] = x[0] * x[1] * x[2] * x[3];
}
if (mode == 1 || mode == 2)
{
cjac[1]             = x[1] * x[2] * x[3];
cjac[ncnln + 1]     = x[0] * x[2] * x[3];
cjac[2 * ncnln + 1] = x[0] * x[1] * x[3];
cjac[3 * ncnln + 1] = x[0] * x[1] * x[2];
}
}
return;
}
```