tutorial2.cpp

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#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#include <string.h>
#include <iostream>
#include "conopticpp.h"
 
class Tut2_ModelData : public ConoptModelData
{
public:
   Tut2_ModelData()
      : ConoptModelData()
   {
   }

   void buildModel()
   {
      /*                                                               */
      /*   Information about Variables:                                */
      /*   Default: Lower = -Inf, Curr = 0, and Upper = +inf.          */
      /*   Default: the status information in Vsta is not used.        */
      /*                                                               */
      /*   Lower bound on L   = X[0] = 0.1 and initial value = 0.5:    */
      /*                                                               */
      addVariable(0.1, CONOPT_INF, 0.5);
      /*                                                               */
      /*   Lower bound on INP = X[1] = 0.1 and initial value = 0.5:    */
      /*                                                               */
      addVariable(0.1, CONOPT_INF, 0.5);
      /*                                                               */
      /*   Lower bound on OUT = X[2] and P = X[3] are both 0 and the   */
      /*   default initial value of 0 is used:                         */
      /*                                                               */
      addVariable(0., CONOPT_INF);
      addVariable(0., CONOPT_INF);
      /*                                                               */
      /*   Information about Constraints:                              */
      /*   Default: Rhs = 0                                            */
      /*   Default: the status information in Esta and the function    */
      /*            value in FV are not used.                          */
      /*   Default: Type: There is no default.                         */
      /*            0 = Equality,                                      */
      /*            1 = Greater than or equal,                         */
      /*            2 = Less than or equal,                            */
      /*            3 = Non binding.                                   */
      /*                                                               */
      /*   Constraint 0 (Objective)                                    */
      /*   Rhs = -0.1 and type Non binding                             */
      /*                                                               */
      addConstraint(ConoptConstraintType::Free, -0.1, {0, 1, 2, 3}, {-1, -1, 0, 0}, {0, 0, 1, 1});
      /*                                                               */
      /*   Constraint 1 (Production Function)                          */
      /*   Rhs = 0 and type Equality                                   */
      /*                                                               */
      addConstraint(ConoptConstraintType::Eq, 0.0, {0, 1, 2}, {0, 0, -1}, {1, 1, 0});
      /*                                                               */
      /*   Constraint 2 (Price equation)                               */
      /*   Rhs = 4.0 and type Equality                                 */
      /*                                                               */
      addConstraint(ConoptConstraintType::Eq, 4.0, {2, 3}, {1, 2}, {0, 0});
 
      /* setting the objective constraint */
      setObjectiveElement(ConoptObjectiveElement::Constraint, 0);
 
      /* setting the optimisation direction */
      setOptimizationSense(ConoptSense::Maximize);
 
      /* setting the structure of the hessian */
      setSDLagrangianStructure({0, 1, 1, 3}, {0, 0, 1, 2});
   }

   int FDEval(const double x[], double* g, double jac[], int rowno, const int jacnum[], int mode, int ignerr,
      int* errcnt, int numvar, int numjac, int thread)
   {
      /*                                                                   */
      /*   Declare local copies of the optimization variables. This is     */
      /*   just for convenience to make the expressions easier to read.    */
      /*                                                                   */
      double L, Inp, Out, P;
      /*                                                                   */
      /*   Declare parameters and their data values.                       */
      /*                                                                   */
      double Al   = 0.16;
      double Ak   = 2.0;
      double Ainp = 0.16;
      double Rho  = 1.0;
      double K    = 4.0;
      double hold1, hold2, hold3;
 
      /*                                                                   */
      /*   Move the optimization variables from the X vector to a set      */
      /*   of local variables with the same names as the variables in      */
      /*   the model description. This is not necessary, but it should make*/
      /*   the equations easier to recognize.                              */
      /*   This time we work with the C numbering convention               */
      /*                                                                   */
      L   = x[0];
      Inp = x[1];
      Out = x[2];
      P   = x[3];
      /*                                                                   */
      /*   Row 0: the objective function is nonlinear                      */
      /*                                                                   */
 
      if ( rowno == 0 ) {
         /*                                                                   */
         /*   Mode = 1 or 3. Function value: G = P * Out                      */
         /*                                                                   */
         if ( mode == 1 || mode == 3 )
            *g    = P * Out;
         /*                                                                   */
         /*   Mode = 2 or 3: Derivative values:                               */
         /*                                                                   */
         if ( mode == 2 || mode == 3 ) {
            jac[2] = P;    /* derivative w.r.t. Out = x[2]               */
            jac[3] = Out;  /* derivative w.r.t. P   = x[3]               */
         }
      }
      /*                                                                   */
      /*   Row 1: The production function is nonlinear                     */
      /*                                                                   */
      else if ( rowno == 1 ) {
         /*                                                                   */
         /*   Compute some common terms                                       */
         /*                                                                   */
         hold1 = (Al*pow(L,(-Rho)) + Ak*pow(K,(-Rho)) + Ainp*pow(Inp,(-Rho)));
         hold2 = pow(hold1,( -1./Rho ));
         /*                                                                   */
         /*   Mode = 1 or 3: Function value                                   */
         /*                                                                   */
         if ( mode == 1 || mode == 3 )
            *g = hold2;
         /*                                                                   */
         /*   Mode = 2 or 3: Derivatives                                      */
         /*                                                                   */
         if ( mode == 2 || mode == 3 ) {
            hold3  = hold2 / hold1;
            jac[0] = hold3 * Al   * pow(L  ,(-Rho-1.)); /* derivative w.r.t. L   = x[0]  */
            jac[1] = hold3 * Ainp * pow(Inp,(-Rho-1.)); /* derivative w.r.t. Inp = x[1]  */
         }
      }
      /*                                                                   */
      /*   Row = 2: The row is linear and will not be called.              */
      /*                                                                   */
 
      return 0;
   }

   int SDLagrVal(const double x[], const double u[], const int hsrw[], const int hscl[], double hsvl[],
      int* nodrv, int numvar, int numcon, int nhess)
   {
   /*
     Declare local copies of the optimization variables. This is
     just for convenience to make the expressions easier to read.        */
 
      double L, Inp, Out, P;
    /*                                                                   */
    /*   Declare parameters and their data values.                       */
    /*                                                                   */
      double Al   = 0.16;
      double Ak   = 2.0;
      double Ainp = 0.16;
      double Rho  = 1.0;
      double K    = 4.0;
      double hold1, hold2, hold3, hold4;
      int    i;
 
   /*  Normal Evaluation mode                                            */
 
      hsvl[3] = u[0]; /* Second derivative of constraint 0 is 1       */
      if ( u[1] != 0.0 ) {
         L   = x[0];
         Inp = x[1];
         Out = x[2];
         P   = x[3];
         hold1 = (Al*pow(L,-Rho) + Ak*pow(K,-Rho) + Ainp*pow(Inp,-Rho));
         hold2 = pow( hold1,-1.0/Rho);
         hold3 = hold2 / hold1;
   /*
     The code for the first derivative was:
           jac(1) = hold3 * Al   * L   ** (-Rho-1.0)
           jac(2) = hold3 * Ainp * Inp ** (-Rho-1.0)
     Define Hold4 as the derivative of Hold3 with respect to Hold1       */
 
        hold4 = hold3 / hold1 * (-1.0/Rho-1.0);
   /*
     The second derivatives are computed as:
     (1) The derivative of Hold3 multiplied by the other terms PLUS
     (2) Hold3 multiplied by the derivative of the other terms
     where the derivative of Hold3 is Hold4 * the derivative of Hold1
     with respect to the variable in question.                           */
 
         hsvl[0] = hold4 * (-Rho) * pow(Al*pow(L,-Rho-1.0),2) +
                   hold3 * Al   * (-Rho-1.0)*pow(L,-Rho-2.0);
         hsvl[1] = hold4 * (-Rho) * (Al*pow(L,-Rho-1.0)) *
                                    (Ainp*pow(Inp,-Rho-1.0));
         hsvl[2] = hold4 * (-Rho) * pow(Ainp*pow(Inp,-Rho-1.0),2) +
                   hold3 * Ainp * (-Rho-1.0)*pow(Inp,-Rho-2.0);
 
   /*  Scale the derivatives with the Lagrange multiplier, u[1]:         */
 
         for ( i = 0; i < 3; i++ )
            hsvl[i] = hsvl[i] * u[1];
      }
 
      (void)P;
      (void)Out;
 
      return 0;
   }
 
};
 
#include "std.cpp"

int main(int argc, char** argv)
{
   int COI_Error = 0;
 
   // getting the program name from the executable path
   std::string pname = getProgramName(argv[0]);
 
   // initialising the Conopt Object
   ConoptCpp conopt(pname);
   Tut2_ModelData modeldata;
   Tut_MessageHandler msghandler(pname);
 
   // adding the message handler to the conopt interface
   conopt.setMessageHandler(msghandler);
 
   // building the model
   modeldata.buildModel();
 
   // loading the model in the conopt object
   conopt.loadModel(modeldata);
 
#if defined(LICENSE_INT_1) && defined(LICENSE_INT_2) && defined(LICENSE_INT_3) && defined(LICENSE_TEXT)
   std::string license = LICENSE_TEXT;
   COI_Error +=  conopt.setLicense(LICENSE_INT_1, LICENSE_INT_2, LICENSE_INT_3, license);
#endif
 
   if ( COI_Error ) {
      conopt.sendMessage("Skipping COI_Solve due to setup errors. COI_Error = " + std::to_string(COI_Error));
      cpp_log(conopt, "Skipping Solve due to setup errors", COI_Error );
      }
 
   COI_Error =  conopt.solve();           /* Optimize                      */
 
   conopt.sendMessage("After solving. COI_Error = " + std::to_string(COI_Error));
   if ( conopt.modelStatus() != 2 || conopt.solutionStatus() != 1 )
      cpp_log(conopt, "Incorrect Model or Solver Status", -1);
   else if ( fabs( conopt.objectiveValue() - 0.572943 ) > 0.000001 )
      cpp_log(conopt, "Incorrect objective returned", -1);
 
   conopt.printStatus();
 
   cpp_log(conopt, "Successful Solve", COI_Error );
}