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# dense_c++.cpp

    /* Copyright 2025, 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
       already have your data in this format.
    */

    #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];
        model.addConstr(lhs, sense[i], rhs[i]);
      }

      GRBQuadExpr obj = 0;

      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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