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### dense_c++.cpp

/* Copyright 2022, Gurobi Optimization, LLC */

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

minimize    x + y + x^2 + x*y + y^2 + y*z + z^2
subject to  x + 2 y + 3 z >= 4
x +   y       >= 1
x, y, z non-negative

The example illustrates the use of dense matrices to store A and Q
(and dense vectors for the other relevant data).  We don't recommend
that you use dense matrices, but this example may be helpful if you
*/

#include "gurobi_c++.h"
using namespace std;

static bool
dense_optimize(GRBEnv* env,
int     rows,
int     cols,
double* c,     /* linear portion of objective function */
double* Q,     /* quadratic portion of objective function */
double* A,     /* constraint matrix */
char*   sense, /* constraint senses */
double* rhs,   /* RHS vector */
double* lb,    /* variable lower bounds */
double* ub,    /* variable upper bounds */
char*   vtype, /* variable types (continuous, binary, etc.) */
double* solution,
double* objvalP)
{
GRBModel model = GRBModel(*env);
int i, j;
bool success = false;

/* Add variables to the model */

GRBVar* vars = model.addVars(lb, ub, NULL, vtype, NULL, cols);

/* Populate A matrix */

for (i = 0; i < rows; i++) {
GRBLinExpr lhs = 0;
for (j = 0; j < cols; j++)
if (A[i*cols+j] != 0)
lhs += A[i*cols+j]*vars[j];
}

for (j = 0; j < cols; j++)
obj += c[j]*vars[j];
for (i = 0; i < cols; i++)
for (j = 0; j < cols; j++)
if (Q[i*cols+j] != 0)
obj += Q[i*cols+j]*vars[i]*vars[j];

model.setObjective(obj);

model.optimize();

model.write("dense.lp");

if (model.get(GRB_IntAttr_Status) == GRB_OPTIMAL) {
*objvalP = model.get(GRB_DoubleAttr_ObjVal);
for (i = 0; i < cols; i++)
solution[i] = vars[i].get(GRB_DoubleAttr_X);
success = true;
}

delete[] vars;

return success;
}

int
main(int   argc,
char *argv[])
{
GRBEnv* env = 0;
try {
env = new GRBEnv();
double c[] = {1, 1, 0};
double  Q[3][3] = {{1, 1, 0}, {0, 1, 1}, {0, 0, 1}};
double  A[2][3] = {{1, 2, 3}, {1, 1, 0}};
char    sense[] = {'>', '>'};
double  rhs[]   = {4, 1};
double  lb[]    = {0, 0, 0};
bool    success;
double  objval, sol[3];

success = dense_optimize(env, 2, 3, c, &Q[0][0], &A[0][0], sense, rhs,
lb, NULL, NULL, sol, &objval);

cout << "optimal=" << success << " x: " << sol[0] << " y: " << sol[1] << " z: " << sol[2] << endl;

} catch(GRBException e) {
cout << "Error code = " << e.getErrorCode() << endl;
cout << e.getMessage() << endl;
} catch(...) {
cout << "Exception during optimization" << endl;
}

delete env;
return 0;
}


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