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bilinear_c.c
/* Copyright 2023, 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 */
error = GRBloadenv(&env, "bilinear.log");
if (error) goto QUIT;
/* Create an empty model */
error = GRBnewmodel(env, &model, "bilinear", 0, NULL, NULL, NULL, NULL,
NULL);
if (error) goto QUIT;
/* Add variables */
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;
}
