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nag_opt_lp (e04mfc) Example Program Optional Parameters

Following options for e04mfc are read by e04xyc.

begin e04mfc

 print_level = Nag_Soln /* Print solution only */
 ftol = 1e-10           /* Set feasiblity tolerance */

end

nag_opt_lp (e04mfc) Example Program Results

Parameters to e04mfc
--------------------

Linear constraints............   5    Number of variables...........   3

prob....................    Nag_LP    start...................  Nag_Cold
ftol....................  1.05e-08    reset_ftol..............         5
fcheck..................        50    crash_tol...............  1.00e-02
inf_bound...............  1.00e+25    inf_step................  1.00e+25
max_iter................        50    machine precision.......  1.11e-16
optim_tol...............  1.72e-13    min_infeas.............. Nag_FALSE
print_level......... Nag_Soln_Iter
outfile.................    stdout

Memory allocation:
state...................       Nag
ax......................       Nag    lambda..................       Nag

Results from e04mfc:
-------------------

  Itn Jdel  Jadd   Step    Ninf  Sinf/Obj    Bnd  Lin  Nart  Nrz  Norm Gz

   0   0     0    0.0e+00   1   1.9369e+02    0    1    2     0   1.96e+01
   1   2 A   6 L  5.0e-01   0   7.2049e-01    0    2    1     0   4.00e-02
   2   6 L   8 L  1.1e+01   0  -2.2109e+02    0    2    1     0   4.98e-01
   3   1 A   7 L  5.4e+02   0  -3.5500e+02    0    3    0     0   0.00e+00

Final solution:

  Varbl State    Value      Lower Bound  Upper Bound    Lagr Mult    Residual

 V   1    FR   7.50000e+01  -7.5000e+01   None       0.000e+00   1.500e+02
 V   2    FR  -2.50000e+02  -1.0000e+03   None       0.000e+00   7.500e+02
 V   3    FR  -1.00000e+01  -2.5000e+01   None       0.000e+00   1.500e+01

   LCon  State    Value     Lower Bound  Upper Bound    Lagr Mult    Residual

 L   1    EQ  -4.21428e-13   0.0000e+00   0.0000e+00   -1.300e-01  -4.214e-13
 L   2    FR  -4.20000e+02  -6.0000e+02   None       0.000e+00   1.800e+02
 L   3    FR   1.50000e+03   0.0000e+00   None       0.000e+00   1.500e+03
 L   4    LL  -5.00000e+02  -5.0000e+02   None       2.500e-01   5.684e-14
 L   5    LL  -1.00000e+03  -1.0000e+03   None       2.300e-01   1.137e-13

Exit after 3 iterations.

Optimal LP solution found.

Final LP objective value =  -3.5500000e+02

Re-solve problem with output of iteration results suppressed and ftol = 1.0e-10.

Optional parameter setting for e04mfc.
--------------------------------------

Option file: e04mfce.opt

print_level set to Nag_Soln
ftol set to 1.00e-10

Parameters to e04mfc
--------------------

Linear constraints............   5    Number of variables...........   3

prob....................    Nag_LP    start...................  Nag_Cold
ftol....................  1.00e-10    reset_ftol..............         5
fcheck..................        50    crash_tol...............  1.00e-02
inf_bound...............  1.00e+25    inf_step................  1.00e+25
max_iter................        50    machine precision.......  1.11e-16
optim_tol...............  1.72e-13    min_infeas.............. Nag_FALSE
print_level.........      Nag_Soln
outfile.................    stdout

Memory allocation:
state...................       Nag
ax......................       Nag    lambda..................       Nag

Final solution:

  Varbl State    Value      Lower Bound  Upper Bound    Lagr Mult    Residual

 V   1    FR   7.50000e+01  -7.5000e+01   None       0.000e+00   1.500e+02
 V   2    FR  -2.50000e+02  -1.0000e+03   None       0.000e+00   7.500e+02
 V   3    FR  -1.00000e+01  -2.5000e+01   None       0.000e+00   1.500e+01

   LCon  State    Value     Lower Bound  Upper Bound    Lagr Mult    Residual

 L   1    EQ   3.59843e-13   0.0000e+00   0.0000e+00   -1.300e-01   3.598e-13
 L   2    FR  -4.20000e+02  -6.0000e+02   None       0.000e+00   1.800e+02
 L   3    FR   1.50000e+03   0.0000e+00   None       0.000e+00   1.500e+03
 L   4    LL  -5.00000e+02  -5.0000e+02   None       2.500e-01   0.000e+00
 L   5    LL  -1.00000e+03  -1.0000e+03   None       2.300e-01   1.137e-13

Exit after 2 iterations.

Optimal LP solution found.

Final LP objective value =  -3.5500000e+02

/* nag_opt_lp (e04mfc) Example Program.
 *
 * CLL6I261D/CLL6I261DL Version.
 *
 * Copyright 2017 Numerical Algorithms Group.
 *
 * Mark 26.1, 2017.
 */

/* This sample linear program (LP) is a portfolio investment problem
 * (see Chapter 7, pp 258--262 of ``Numerical Linear Algebra and
 * Optimization'', by Gill, Murray and Wright, Addison Wesley, 1991).
 * The problem involves the rearrangement of a portfolio of three
 * stocks, Glitter, Risky and Trusty, so that the net worth of the
 * investor is maximized.
 * The problem is characterized by the following data:
 *                           Glitter     Risky        Trusty
 * 1990 Holdings                75       1000           25
 * 1990 Priceshare($)           20          2          100
 * 2099 Priceshare($)           18          3          102
 * 2099 Dividend                 5          0            2
 *
 * The variables x[0], x[1] and x[2] represent the change in each of
 * the three stocks.
 */

#include <nag.h>
#include <stdio.h>
#include <nag_stdlib.h>
#include <nag_string.h>
#include <nage04.h>

#define A(I, J) a[(I) *tda + J]

int main(void)
{
  const char *optionsfile = "e04mfce.opt";
  Integer exit_status = 0;
  Nag_Boolean print;
  Integer n, nbnd, nclin, tda;
  Nag_E04_Opt options;
  double *a = 0, bigbnd, *bl = 0, *bu = 0, *cvec = 0, objf, *x = 0;
  Nag_Comm comm;
  NagError fail;

  INIT_FAIL(fail);

  printf("nag_opt_lp (e04mfc) Example Program Results\n");
  /* Set the actual problem dimensions.
   * n      = the number of variables.
   * nclin  = the number of general linear constraints (may be 0).
   */
  n = 3;
  nclin = 5;
  nbnd = n + nclin;
  if (n >= 1 && nclin >= 0) {
    if (!(x = nAG_ALLOC(n, double)) ||
        !(cvec = nAG_ALLOC(n, double)) ||
        !(a = nAG_ALLOC(nclin * n, double)) ||
        !(bl = nAG_ALLOC(nbnd, double)) || !(bu = nAG_ALLOC(nbnd, double)))
    {
      printf("Allocation failure\n");
      exit_status = -1;
      goto END;
    }
    tda = n;
  }
  else {
    printf("Invalid n or nclin.\n");
    exit_status = 1;
    return exit_status;
  }

  /* Define the value used to denote ``infinite'' bounds. */
  bigbnd = 1e+25;

  /* Objective function:  maximize  5*X[0] + 2*X[2], or equivalently,
   * minimize -5*X[0] - 2*X[2].
   */
  cvec[0] = -5.0;
  cvec[1] = 0.0;
  cvec[2] = -2.0;

  /* a  = the general constraint matrix.
   * bl = the lower bounds on  x  and  A*x.
   * bu = the upper bounds on  x  and  A*x.
   * x  = the initial estimate of the solution.
   *
   * A nonnegative amount of stock must be present after rearrangement.
   * For Glitter:  x[0] + 75 >= 0.
   */
  bl[0] = -75.0;
  bu[0] = bigbnd;

  /* For Risky:    x[1] + 1000 >= 0.0 */
  bl[1] = -1000.0;
  bu[1] = bigbnd;

  /* For Trusty:   x[2] + 25 >= 0.0 */
  bl[2] = -25.0;
  bu[2] = bigbnd;

  /* The current value of the portfolio must be the same after
   * rearrangement, i.e.,
   *  20*(75+x[0]) + 2*(1000+x[1]) + 100*(25+x[2]) = 6000, or
   *  20*x[0] + 2*x[1] + 100*x[2] = 0.
   */
  A(0, 0) = 20.0;
  A(0, 1) = 2.0;
  A(0, 2) = 100.0;
  bl[n] = 0.0;
  bu[n] = 0.0;

  /* The value of the portfolio must increase by at least 5 per cent
   * at the end of the year, i.e.,
   * 18*(75+x[0]) + 3*(1000+x[1]) + 102*(25+x[2]) >= 6300, or
   * 18*x[0] + 3*x[1] + 102*x[2] >= -600.
   */
  A(1, 0) = 18.0;
  A(1, 1) = 3.0;
  A(1, 2) = 102.0;
  bl[n + 1] = -600.0;
  bu[n + 1] = bigbnd;

  /* There are three ``balanced portfolio'' constraints.  The value of
   * a stock must constitute at least a quarter of the total final
   * value of the portfolio.  After rearrangement, the value of the
   * portfolio after is  20*(75+x[0]) + 2*(1000+x[1]) + 100*(25+x[2]).
   *
   * If Glitter is to constitute at least a quarter of the final
   * portfolio, then  15*x[0] - 0.5*x[1] - 25*x[2] >= 0.
   */
  A(2, 0) = 15.0;
  A(2, 1) = -0.5;
  A(2, 2) = -25.0;
  bl[n + 2] = 0.0;
  bu[n + 2] = bigbnd;

  /* If Risky is to constitute at least a quarter of the final
   * portfolio, then  -5*x[0] + 1.5*x[1] - 25*x[2] >= -500.
   */
  A(3, 0) = -5.0;
  A(3, 1) = 1.5;
  A(3, 2) = -25.0;
  bl[n + 3] = -500.0;
  bu[n + 3] = bigbnd;

  /* If Trusty is to constitute at least a quarter of the final
   * portfolio, then  -5*x[0] - 0.5*x[1] + 75*x[2] >= -1000.
   */
  A(4, 0) = -5.0;
  A(4, 1) = -0.5;
  A(4, 2) = 75.0;
  bl[n + 4] = -1000.0;
  bu[n + 4] = bigbnd;

  /* Set the initial estimate of the solution.
   * This portfolio is infeasible.
   */
  x[0] = 10.0;
  x[1] = 20.0;
  x[2] = 100.0;

  /* Initialize options structure to null values. */
  /* nag_opt_init (e04xxc).
   * Initialization function for option setting
   */
  nag_opt_init(&options);
  options.inf_bound = bigbnd;

  /* Solve the problem. */
  /* nag_opt_lp (e04mfc), see above. */
  fflush(stdout);
  nag_opt_lp(n, nclin, a, tda, bl, bu, cvec,
             x, &objf, &options, &comm, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_opt_lp (e04mfc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  /* Re-solve the problem with some additonal options. */

  printf("Re-solve problem with output of iteration results");
  printf(" suppressed and ftol = 1.0e-10.\n");

  /* Read additional options from a file. */
  print = Nag_TRUE;
  /* nag_opt_read (e04xyc).
   * Read options from a text file
   */
  fflush(stdout);
  nag_opt_read("e04mfc", optionsfile, &options, print, "stdout", &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_opt_read (e04xyc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  /* Reset starting point */
  x[0] = 0.0;
  x[1] = 0.0;
  x[2] = 0.0;

  /* Solve the problem again. */
  /* nag_opt_lp (e04mfc), see above. */
  nag_opt_lp(n, nclin, a, tda, bl, bu, cvec,
             x, &objf, &options, &comm, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_opt_lp (e04mfc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  /* Free memory allocated by nag_opt_lp (e04mfc) to pointers in options. */
  /* nag_opt_free (e04xzc).
   * Memory freeing function for use with option setting
   */
  nag_opt_free(&options, "all", &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_opt_free (e04xzc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

END:
  nAG_FREE(x);
  nAG_FREE(cvec);
  nAG_FREE(a);
  nAG_FREE(bl);
  nAG_FREE(bu);

  return exit_status;
}