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### bilinear_c.c

/* Copyright 2021, Gurobi Optimization, LLC */

/* This example formulates and solves the following simple bilinear model:

maximize    x
subject to  x + y + z <= 10
x * y <= 2          (bilinear inequality)
x * z + y * z == 1  (bilinear equality)
x, y, z non-negative (x integral in second version)
*/

#include <stdlib.h>
#include <stdio.h>
#include "gurobi_c.h"

int
main(int   argc,
char *argv[])
{
GRBenv   *env   = NULL;
GRBmodel *model = NULL;
int       error = 0;
double    sol[3];
int       ind[3];
double    val[3];
double    obj[] = {1, 0, 0};
int       qrow[2];
int       qcol[2];
double    qval[2];
int       optimstatus;
double    objval;

/* Create environment */

if (error) goto QUIT;

/* Create an empty model */

error = GRBnewmodel(env, &model, "bilinear", 0, NULL, NULL, NULL, NULL,
NULL);
if (error) goto QUIT;

error = GRBaddvars(model, 3, 0, NULL, NULL, NULL, obj, NULL, NULL, NULL,
NULL);
if (error) goto QUIT;

/* Change sense to maximization */

error = GRBsetintattr(model, GRB_INT_ATTR_MODELSENSE, GRB_MAXIMIZE);
if (error) goto QUIT;

/* Linear constraint: x + y + z <= 10 */

ind[0] = 0; ind[1] = 1; ind[2] = 2;
val[0] = 1; val[1] = 1; val[2] = 1;

error = GRBaddconstr(model, 3, ind, val, GRB_LESS_EQUAL, 10.0, "c0");
if (error) goto QUIT;

/* Bilinear inequality: x * y <= 2 */

qrow[0] = 0; qcol[0] = 1; qval[0] = 1.0;

error = GRBaddqconstr(model, 0, NULL, NULL, 1, qrow, qcol, qval,
GRB_LESS_EQUAL, 2.0, "bilinear0");
if (error) goto QUIT;

/* Bilinear equality: x * z + y * z == 1 */

qrow[0] = 0; qcol[0] = 2; qval[0] = 1.0;
qrow[1] = 1; qcol[1] = 2; qval[1] = 1.0;

error = GRBaddqconstr(model, 0, NULL, NULL, 2, qrow, qcol, qval,
GRB_EQUAL, 1, "bilinear1");
if (error) goto QUIT;

/* Optimize model - this will fail since we need to set NonConvex to 2 */

error = GRBoptimize(model);
if (!error) {
printf("Should have failed!\n");
goto QUIT;
}

/* Set parameter and solve again */

error = GRBsetintparam(GRBgetenv(model), GRB_INT_PAR_NONCONVEX, 2);
if (error) goto QUIT;

error = GRBoptimize(model);
if (error) goto QUIT;

/* Write model to 'bilinear.lp' */

error = GRBwrite(model, "bilinear.lp");
if (error) goto QUIT;

/* Capture solution information */

error = GRBgetintattr(model, GRB_INT_ATTR_STATUS, &optimstatus);
if (error) goto QUIT;

error = GRBgetdblattr(model, GRB_DBL_ATTR_OBJVAL, &objval);
if (error) goto QUIT;

error = GRBgetdblattrarray(model, GRB_DBL_ATTR_X, 0, 3, sol);
if (error) goto QUIT;

printf("\nOptimization complete\n");
if (optimstatus == GRB_OPTIMAL) {
printf("Optimal objective: %.4e\n", objval);

printf("  x=%.2f, y=%.2f, z=%.2f\n", sol[0], sol[1], sol[2]);
} else if (optimstatus == GRB_INF_OR_UNBD) {
printf("Model is infeasible or unbounded\n");
} else {
printf("Optimization was stopped early\n");
}

/* Now constrain 'x' to be integral and solve again */

error = GRBsetcharattrelement(model, GRB_CHAR_ATTR_VTYPE, 0, GRB_INTEGER);
if (error) goto QUIT;

error = GRBoptimize(model);
if (error) goto QUIT;

/* Capture solution information */

error = GRBgetintattr(model, GRB_INT_ATTR_STATUS, &optimstatus);
if (error) goto QUIT;

error = GRBgetdblattr(model, GRB_DBL_ATTR_OBJVAL, &objval);
if (error) goto QUIT;

error = GRBgetdblattrarray(model, GRB_DBL_ATTR_X, 0, 3, sol);
if (error) goto QUIT;

printf("\nOptimization complete\n");
if (optimstatus == GRB_OPTIMAL) {
printf("Optimal objective: %.4e\n", objval);

printf("  x=%.2f, y=%.2f, z=%.2f\n", sol[0], sol[1], sol[2]);
} else if (optimstatus == GRB_INF_OR_UNBD) {
printf("Model is infeasible or unbounded\n");
} else {
printf("Optimization was stopped early\n");
}

QUIT:

/* Error reporting */

if (error) {
printf("ERROR: %s\n", GRBgeterrormsg(env));
exit(1);
}

/* Free model */

GRBfreemodel(model);

/* Free environment */

GRBfreeenv(env);

return 0;
}