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Re: [Bug-glpk] Re: Bug report for GLPK


From: Andrew Makhorin
Subject: Re: [Bug-glpk] Re: Bug report for GLPK
Date: Tue, 23 Mar 2010 21:48:00 +0300

> Looking thru your bug report I found that you perform perturbation
> of the constraint matrix by adding 1e-15 to all its elements.

Oops, sorry. You do not change exact zeros.

However, I didn't see in your report (see the matlab output) the
difference between A and \tilde{A}, and between b and \tilde{b}, i.e.
1e-15 looks to be too small for perturbation.

I solved your instance with glpsol 4.43 (see below) I found nothing
wrong.

------------------------------------------------------------------------
Minimize
   obj: 1 x1 + 0 x2

Subject To
e1:  1.000000000000000 x1 - 0.666666666666667 x2 <=  0.333333333333333
e2:  0.166666666666667 x1 + 1.000000000000000 x2 <=  0.500000000000000
e3: -0.833333333333333 x1 - 1.000000000000000 x2 <= -0.500000000000000
e4: -0.666666666666667 x1 + 0.333333333333333 x2 <=  0
e5:  0.000000000000000 x1 - 1.333333333333333 x2 <= -0.333333333333333
e6:  1.000000000000000 x1 + 0.666666666666667 x2 <=  0.666666666666667
e7:  1.000000000000000 x1 + 1.000000000000000 x2 <=  1.000000000000000
e8: -1.000000000000000 x1 +                 0 x2 <=  0
e9:                  0 x1 - 1.000000000000000 x2 <=  0

End
------------------------------------------------------------------------
GLPSOL: GLPK LP/MIP Solver, v4.43
Parameter(s) specified in the command line:
 --lp --nopresol test.txt -o test.sol --log test.log
Reading problem data from `test.txt'...
9 rows, 2 columns, 15 non-zeros
16 lines were read
Scaling...
 A: min|aij| =  1.667e-01  max|aij| =  1.333e+00  ratio =  8.000e+00
Problem data seem to be well scaled
Constructing initial basis...
Size of triangular part = 9
GLPK Simplex Optimizer, v4.43
9 rows, 2 columns, 15 non-zeros
      0: obj =   0.000000000e+00  infeas =  8.333e-01 (0)
*     3: obj =   1.764705882e-01  infeas =  0.000e+00 (0)
OPTIMAL SOLUTION FOUND
Time used:   0.0 secs
Memory used: 0.0 Mb (31851 bytes)
Writing basic solution to `test.sol'...
------------------------------------------------------------------------
Problem:
Rows:       9
Columns:    2
Non-zeros:  15
Status:     OPTIMAL
Objective:  obj = 0.1764705882 (MINimum)

   No.   Row name   St   Activity     Lower bound   Upper bound    Marginal
------ ------------ -- ------------- ------------- ------------- -------------
     1 e1           B     -0.0588235                    0.333333 
     2 e2           B       0.382353                         0.5 
     3 e3           NU          -0.5                        -0.5     -0.352941 
     4 e4           NU             0                           0      -1.05882 
     5 e5           B      -0.470588                   -0.333333 
     6 e6           B       0.411765                    0.666667 
     7 e7           B       0.529412                           1 
     8 e8           B      -0.176471                           0 
     9 e9           B      -0.352941                           0 

   No. Column name  St   Activity     Lower bound   Upper bound    Marginal
------ ------------ -- ------------- ------------- ------------- -------------
     1 x1           B       0.176471             0               
     2 x2           B       0.352941             0               

Karush-Kuhn-Tucker optimality conditions:

KKT.PE: max.abs.err = 5.55e-17 on row 2
        max.rel.err = 3.15e-17 on row 2
        High quality

KKT.PB: max.abs.err = 0.00e+00 on row 0
        max.rel.err = 0.00e+00 on row 0
        High quality

KKT.DE: max.abs.err = 0.00e+00 on column 0
        max.rel.err = 0.00e+00 on column 0
        High quality

KKT.DB: max.abs.err = 0.00e+00 on row 0
        max.rel.err = 0.00e+00 on row 0
        High quality

End of output





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