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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