/* nag_opt_handle_print (e04ryc) Example Program.
*
* Copyright 2024 Numerical Algorithms Group.
*
* Mark 30.1, 2024.
*/
/* Demonstrate the life-cycle of a handle of a typical BMI-SDP problem
* by printing the evolution of the HANDLE in certain stages to
* the standard output.
*/
#include <nag.h>
#include <stdio.h>
int main(void) {
Integer exit_status = 0;
Integer dima, idblk, inform, nblk, nnzasum, nvar;
double a[6], bl[2], bu[2], cvec[2], rinfo[32], stats[32], x[2];
Integer icola[6], irowa[6], nnza[3], qi[1], qj[1];
void *h = 0;
/* Nag Types */
Nag_FileID fileid;
NagError fail;
printf("nag_opt_handle_print (e04ryc) Example Program Results\n\n");
fflush(stdout);
/* Get Nag_FileID associated with the standard output by
* nag_file_open (x04aac). */
nag_file_open(NULL, 1, &fileid, NAGERR_DEFAULT);
/* nag_opt_handle_init (e04rac).
* Initialize an empty problem handle with 2 variables. */
nvar = 2;
nag_opt_handle_init(&h, nvar, NAGERR_DEFAULT);
/* Anything can be defined at this phase. */
printf("Freshly created handle\n");
fflush(stdout);
/* nag_opt_handle_print (e04ryc).
* Print information currently stored in the handle. */
nag_opt_handle_print(h, fileid, "Overview", NAGERR_DEFAULT);
/* nag_opt_handle_set_linobj (e04rec).
* Define linear objective (min y). */
cvec[0] = 0.0;
cvec[1] = 1.0;
nag_opt_handle_set_linobj(h, nvar, cvec, NAGERR_DEFAULT);
/* nag_opt_handle_set_simplebounds (e04rhc).
* Add simple bounds (x>=0, -3<=y<=3) to the problem formulation. */
bl[0] = 0.0;
bu[0] = 1.0e20;
bl[1] = -3.0;
bu[1] = 3.0;
nag_opt_handle_set_simplebounds(h, nvar, bl, bu, NAGERR_DEFAULT);
/* The simple bounds and the objective are set and cannot be changed. */
printf("\nHandle after definition of simple bounds and the objective\n");
fflush(stdout);
nag_opt_handle_print(h, fileid, "Overview,Objective,Simple Bounds",
NAGERR_DEFAULT);
/* Definition of the first (linear) matrix constraint
* ( 1 x-1 y )
* (x-1 3/4 0 ) >= 0
* ( y 0 16 )
* only upper triangles, thus we have matrices
* ( 1 -1 0 ) ( 0 1 0 ) ( 0 0 1 )
* A0 = -( 3/4 0 ), A1 = ( 0 0 ), A2 = ( 0 0 )
* ( 16 ) ( 0 ) ( 0 )
* Note: don't forget the minus at A0 term! */
dima = 3;
nnzasum = 6;
nblk = 1;
idblk = 0;
/* A0 */
irowa[0] = 1;
icola[0] = 1;
a[0] = -1.0;
irowa[1] = 1;
icola[1] = 2;
a[1] = 1.0;
irowa[2] = 2;
icola[2] = 2;
a[2] = -0.75;
irowa[3] = 3;
icola[3] = 3;
a[3] = -16.0;
nnza[0] = 4;
/* A1 */
irowa[4] = 1;
icola[4] = 2;
a[4] = 1.0;
nnza[1] = 1;
/* A2 */
irowa[5] = 1;
icola[5] = 3;
a[5] = 1.0;
nnza[2] = 1;
/* nag_opt_handle_set_linmatineq (e04rnc).
* Add a linear matrix inequality constraint to the problem formulation. */
nag_opt_handle_set_linmatineq(h, nvar, dima, nnza, nnzasum, irowa, icola, a,
nblk, NULL, &idblk, NAGERR_DEFAULT);
/* It is possible to add or extend existing matrix constraints. */
printf("\nHandle after definition of the 1st matrix constraint\n");
fflush(stdout);
nag_opt_handle_print(h, fileid, "Overview,Matrix Constraints",
NAGERR_DEFAULT);
/* Definition of the absolute term and linear part of BMI
* ( x -xy )
* (-xy 1 ) >= 0
* thus
* ( 0 0 ) ( 1 0 )
* A0 = -( 1 ), A1 = ( 0 ), A2 = zero
* Note: don't forget the minus at A0 term! */
dima = 2;
nnzasum = 2;
nblk = 1;
idblk = 0;
/* A0 */
irowa[0] = 2;
icola[0] = 2;
a[0] = -1.0;
nnza[0] = 1;
/* A1 */
irowa[1] = 1;
icola[1] = 1;
a[1] = 1.0;
nnza[1] = 1;
/* A2 */
nnza[2] = 0;
/* nag_opt_handle_set_linmatineq (e04rnc).
* Add another linear matrix inequality which will be extended to BMI. */
nag_opt_handle_set_linmatineq(h, nvar, dima, nnza, nnzasum, irowa, icola, a,
nblk, NULL, &idblk, NAGERR_DEFAULT);
/* It is possible to add or extend existing matrix constraints. */
printf("\nHandle after partial definition of the 2nd matrix constraint\n");
fflush(stdout);
nag_opt_handle_print(h, fileid, "Matrix Constraints", NAGERR_DEFAULT);
/* Extending current matrix constraint (with IDBLK) by bilinear term
* ( 0 -1 )
* Q12 = ( 0 0 ). */
dima = 2;
nnzasum = 1;
nnza[0] = 1;
irowa[0] = 1;
icola[0] = 2;
a[0] = -1.0;
qi[0] = 1;
qj[0] = 2;
/* nag_opt_handle_set_quadmatineq (e04rpc).
* Add a bilinear matrix term. */
nag_opt_handle_set_quadmatineq(h, 1, qi, qj, dima, nnza, nnzasum, irowa,
icola, a, &idblk, NAGERR_DEFAULT);
/* The problem is completely defined. */
printf("\nHandle with the complete problem formulation\n");
fflush(stdout);
nag_opt_handle_print(h, fileid,
"Overview,Matrix Constraints,Multipliers Sizes",
NAGERR_DEFAULT);
nag_opt_handle_print(h, fileid, "Matrix Constraints Detailed",
NAGERR_DEFAULT);
/* Set optional arguments of the solver by calling
* nag_opt_handle_opt_set (e04zmc). */
nag_opt_handle_opt_set(h, "Print Options = No", NAGERR_DEFAULT);
nag_opt_handle_opt_set(h, "Initial X = Automatic", NAGERR_DEFAULT);
/* Options can be printed even outside the solver. */
printf("\n");
fflush(stdout);
nag_opt_handle_print(h, fileid, "Options", NAGERR_DEFAULT);
/* Pass the handle to the solver
* nag_opt_handle_solve_pennon (e04svc). */
INIT_FAIL(fail);
nag_opt_handle_solve_pennon(h, nvar, x, 0, NULL, 0, NULL, 0, NULL, rinfo,
stats, &inform, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_opt_handle_solve_pennon (e04svc).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}
/* After the solver finished. */
printf("\nProblem solved\n");
fflush(stdout);
nag_opt_handle_print(h, fileid, "Overview", NAGERR_DEFAULT);
/* Print the result. */
printf("\nFinal objective function = %f\n", rinfo[0]);
printf("Final x = [%f, %f].\n", x[0], x[1]);
/* nag_opt_handle_free (e04rzc).
* Destroy the problem handle and deallocate all the memory. */
nag_opt_handle_free(&h, NAGERR_DEFAULT);
END:
return exit_status;
}