/********************************************************
  Xpress-BCL C Example Problems
  =============================

  file folioqp.c
  ``````````````
  Modeling a small QP problem
  to perform portfolio optimization.
   -- 1. QP: minimize variance
      2. MIQP: limited number of assets ---

  (c) 2008-2024 Fair Isaac Corporation
      author: S.Heipcke, Dec. 2003, rev. Mar. 2011
********************************************************/

#include <stdio.h>
#include "xprb.h"

#define DATAFILE XPRBDATAPATH "/GS/foliocppqp.dat"

#define TARGET 9                   /* Target yield */
#define MAXNUM 4                   /* Max. number of different assets */

#define NSHARES 10                 /* Number of shares */
#define NNA 4                      /* Number of North-American shares */

double RET[] = {5,17,26,12,8,9,7,6,31,21};  /* Estimated return in investment */
int NA[] = {0,1,2,3};              /* Shares issued in N.-America */
double VAR[NSHARES][NSHARES];      /* Variance/covariance matrix of
                                      estimated returns */

int main(int argc, char **argv)
{
 int s,t;
 XPRBprob prob;
 XPRBctr Variance,Na,Return,Cap,Num;
 XPRBvar frac[NSHARES];            /* Fraction of capital used per share */
 XPRBvar buy[NSHARES];             /* 1 if asset is in portfolio, 0 otherwise */
 FILE *datafile;

 prob = XPRBnewprob("FolioQP");    /* Initialize a new problem in BCL */

/* Read `VAR' data from file */
 datafile=fopen(DATAFILE,"r");
 for(s=0;s<NSHARES;s++)
  XPRBreadarrlinecb(XPRB_FGETS, datafile,200,"g ",VAR[s],NSHARES);
 fclose(datafile);

/***** First problem: unlimited number of assets *****/

/* Create the decision variables */
 for(s=0;s<NSHARES;s++)
  frac[s] = XPRBnewvar(prob, XPRB_PL, XPRBnewname("frac(%d)",s+1), 0, 0.3);

/* Objective: mean variance */
 Variance = XPRBnewctr(prob, "Variance", XPRB_N);
 for(s=0;s<NSHARES;s++)
  for(t=0;t<NSHARES;t++) XPRBaddqterm(Variance, frac[s], frac[t], VAR[s][t]);
 XPRBsetobj(prob, Variance);

/* Minimum amount of North-American values */
 Na = XPRBnewctr(prob, "NA", XPRB_G);
 for(s=0;s<NNA;s++) XPRBaddterm(Na, frac[NA[s]], 1);
 XPRBaddterm(Na, NULL, 0.5);

/* Spend all the capital */
 Cap = XPRBnewctr(prob, "Cap", XPRB_E);
 for(s=0;s<NSHARES;s++) XPRBaddterm(Cap, frac[s], 1);
 XPRBaddterm(Cap, NULL, 1);

/* Target yield */
 Return = XPRBnewctr(prob, "Return", XPRB_G);
 for(s=0;s<NSHARES;s++) XPRBaddterm(Return, frac[s], RET[s]);
 XPRBaddterm(Return, NULL, TARGET);

/* Solve the problem */
 XPRBsetsense(prob, XPRB_MINIM);
 XPRBlpoptimize(prob, "");

/* Solution printing */
 printf("With a target of %d minimum variance is %g\n", TARGET,
        XPRBgetobjval(prob));
 for(s=0;s<NSHARES;s++)
  printf(" %d : %g%%\n", s, XPRBgetsol(frac[s])*100);

/***** Second problem: limit total number of assets *****/

/* Create the decision variables */
 for(s=0;s<NSHARES;s++)
  buy[s] = XPRBnewvar(prob, XPRB_BV, XPRBnewname("buy(%d)",s+1), 0, 1);

/* Limit the total number of assets */
 Num = XPRBnewctr(prob, "Num", XPRB_L);
 for(s=0;s<NSHARES;s++) XPRBaddterm(Num, buy[s], 1);
 XPRBaddterm(Num, NULL, MAXNUM);

/* Linking the variables */
 for(s=0;s<NSHARES;s++) XPRBnewprec(prob, "Link", frac[s], 0, buy[s]);

/* Solve the problem */
 XPRBmipoptimize(prob, "");

/* Solution printing */
 printf("With a target of %d and at most %d assets, minimum variance is %g\n",
        TARGET, MAXNUM, XPRBgetobjval(prob));
 for(s=0;s<NSHARES;s++)
  printf(" %d : %g%% (%g)\n", s, XPRBgetsol(frac[s])*100, XPRBgetsol(buy[s]));

 return 0;
}