/*
#################################################################
# LINDO-API
# Sample Programs
# Copyright (c) 2001-2002
#
# LINDO Systems, Inc. 312.988.7422
# 1415 North Dayton St. info@lindo.com
# Chicago, IL 60622 http://www.lindo.com
#################################################################
File : markow.c
Purpose: Solve a quadratic programming problem.
Model : The Markowitz Portfolio Selection Model
MAXIMIZE r(1)w(1) + ... +r(n)w(n)
st. sum_{ij} Q(i,j)w(i)w(j) <= K
w(1) + ..... + w(n) = 1
w(1), ,w(n) >= 0
where
r(i) : return on asset i
Q(i,j): covariance between the returns of i^th and
j^th assets.
K : a scalar denoting the level of risk of loss.
w(i) : proportion of total budget invested on asset i
Covariance Matrix:
w1 w2 w3 w4
w1 [ 1.00 0.64 0.27 0. ]
w2 [ 0.64 1.00 0.13 0. ]
w3 [ 0.27 0.13 1.00 0. ]
w4 [ 0. 0. 0. 1.00 ]
Returns Vector:
w1 w2 w3 w4
r = [ 0.30 0.20 -0.40 0.20 ]
Risk of Loss Factor:
K = 0.4
*/
#include
#include
#include
#include "lindo.h"
#include "license.h"
/* Define a macro to declare variables for
error checking */
#define APIERRORSETUP \
int nErrorCode; \
char cErrorMessage[LS_MAX_ERROR_MESSAGE_LENGTH] \
/* Define a macro to do our error checking */
#define APIERRORCHECK \
if (nErrorCode) \
{ \
if ( pEnv) \
{ \
LSgetErrorMessage( pEnv, nErrorCode, \
cErrorMessage); \
printf("Errorcode=%d: %s\n", nErrorCode, \
cErrorMessage); \
} else {\
printf( "Fatal Error\n"); \
} \
exit(1); \
} \
/* main entry point */
int main(int argc, char **argv)
{
APIERRORSETUP;
int nM = 2; /* Number of constraints */
int nN = 4; /* Number of assets */
double K = 0.20; /* 1/2 of the risk level*/
/* declare an instance of the LINDO environment object */
pLSenv pEnv;
/* declare an instance of the LINDO model object */
pLSmodel pModel;
/****************************************************************
* Step 1: Create a LINDO environment. MY_LICENSE_KEY in licence.h
* must be defined using the key shipped with your software.
****************************************************************/
pEnv = LScreateEnv ( &nErrorCode, MY_LICENSE_KEY);
if ( nErrorCode == LSERR_NO_VALID_LICENSE)
{
printf( "Invalid License Key!\n");
exit( 1);
}
APIERRORCHECK;
/****************************************************************
* Step 2: Create a model in the environment.
****************************************************************/
pModel = LScreateModel ( pEnv, &nErrorCode);
APIERRORCHECK;
/*****************************************************************
* Step 3: Specify and load the LP portion of the model.
*****************************************************************/
{
/* The direction of optimization */
int objsense = LS_MAX;
/* The objective's constant term */
double objconst = 0.;
/* The coefficients of the objective function are the expected
returns*/
double reward[4] = { .3, .2, -.4, .2};
/* The right-hand sides of the constraints */
double rhs[2] = { K, 1.0 };
/* The constraint types */
char contype[2] = {'L','E'};
/* The number of nonzeros in the constraint matrix */
int Anz = 4;
/* The indices of the first nonzero in each column */
int Abegcol[5] = { 0, 1, 2, 3, Anz};
/* The length of each column. Since we aren't leaving
* any blanks in our matrix, we can set this to NULL */
int *Alencol = NULL;
/* The nonzero coefficients */
double A[4] = { 1., 1., 1., 1.};
/* The row indices of the nonzero coefficients */
int Arowndx[4] = { 1, 1, 1, 1};
/* By default, all variables have a lower bound of zero
* and an upper bound of infinity. Therefore pass NULL
* pointers in order to use these default values. */
double *lb = NULL, *ub = NULL;
/*****************************************************************
* Step 4: Specify and load the quadratic matrix
*****************************************************************/
/* The number of nonzeros in the quadratic matrix */
int Qnz = 7;
/* The nonzero coefficients in the Q-matrix */
double Q[7] = { 1.00, .64, .27,
1.00, .13,
1.00,
1.00} ;
/* Specify the row indices of the nonzero coefficients in the
Q-matrix. */
int Qrowndx[7] = { 0, 0, 0, 0, 0, 0, 0};
/* The indices of variables in the Q-matrix */
int Qcolndx1[7] = { 0, 1, 2, 1, 2, 2, 3};
int Qcolndx2[7] = { 0, 0, 0, 1, 1, 2, 3};
/* Pass the linear portion of the data to problem structure
* by a call to LSloadLPData() */
nErrorCode = LSloadLPData( pModel, nM, nN, objsense, objconst,
reward, rhs, contype,
Anz, Abegcol, Alencol, A, Arowndx,
lb, ub);
APIERRORCHECK;
/* Pass the quadratic portion of the data to problem structure
* by a call to LSloadQCData() */
nErrorCode = LSloadQCData(pModel, Qnz, Qrowndx,
Qcolndx1, Qcolndx2, Q );
APIERRORCHECK;
}
/*****************************************************************
* Step 5: Perform the optimization using the barrier solver
*****************************************************************/
nErrorCode = LSoptimize( pModel, LS_METHOD_BARRIER,NULL);
APIERRORCHECK;
/***************************************************************
* Step 6: Retrieve the solution
***************************************************************/
{
int i;
double W[4], dObj;
/* Get the value of the objective */
nErrorCode = LSgetInfo( pModel, LS_DINFO_POBJ, &dObj) ;
APIERRORCHECK;
printf( "* Objective Value = %10g\n\n", dObj);
/* Get the portfolio */
nErrorCode = LSgetPrimalSolution ( pModel, W);
APIERRORCHECK;
printf ("* Optimal Portfolio : \n");
for (i = 0; i < nN; i++)
printf( "Invest %5.2f percent of total budget in asset %d.\n",
100*W[i],i+1 );
printf ("\n");
}
/***************************************************************
* Step 7: Delete the LINDO environment
*****************************************************************/
nErrorCode = LSdeleteEnv( &pEnv);
/* Wait until user presses the Enter key */
printf("Press ...");
getchar();
}
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