Re: [Help-glpk] different results in glpk api and glpsol version 4.35 on win32 machine

[Andrew Makhorin]

> I hope this is the right place for this question...
> 
> I am trying to solve the problem in the attached lp file and I get
> confusing results. When calling glpsol with "glpsol --cpxlp --interior
> --min --cbg -w temp_solved.txt test_prob_100_lp.txt" I get the results
> that I am expecting. 

The --cbg option affects only the simplex solver.

> When I try to use the API I get numeric
> instability. I did automatic scaling of the data with
> "glp_scale_prob(lp,GLP_SF_AUTO)".

Your lp is well scaled, so the automatic scaling is not needed.

> What's confusing is the fact that the test_prob_100_lp.txt is produced
> by calling glp_write_lp, so the problem is formulated the same way in
> both cases.
> 
> The console output of glpsol is
> 
> D:\Phase unwrapping\C_code\putmcf\Debug>glpsol --cpxlp --interior
> --min -w temp_solved.txt test_prob_100_lp.txt
> glp_read_lp: reading problem data from `test_prob_100_lp.txt'...
> glp_read_lp: 7958 rows, 24014 columns, 47748 non-zeros
> glp_read_lp: 11009 lines were read
> Scaling...
>  A: min|aij| = 1.000e+000  max|aij| = 1.000e+000  ratio = 1.000e+000
> Problem data seem to be well scaled
> glp_interior: original LP problem has 7958 rows and 24014 columns
> glp_interior: transformed LP problem has 7958 rows and 24014 columns
> lpx_interior: A has 47748 non-zeros
> lpx_interior: S has 19825 non-zeros (upper triangle)
> lpx_interior: minimal degree ordering...
> lpx_interior: computing Cholesky factorization...
> lpx_interior: U has 93259 non-zeros
> lpx_interior: guessing initial point...
> Optimization begins...
>   0: obj =  1.887813906e+004; rpi = 1.5e-015; rdi = 2.7e+000; gap = 1.0e+000
>   1: obj =  1.115924070e+004; rpi = 8.0e-016; rdi = 2.7e-001; gap = 1.0e+000
>   2: obj =  2.881199640e+003; rpi = 1.1e-015; rdi = 4.2e-002; gap = 9.8e-001
>   3: obj =  1.001952442e+003; rpi = 1.1e-015; rdi = 2.0e-002; gap = 9.4e-001
>   4: obj =  5.424831020e+002; rpi = 1.8e-015; rdi = 1.1e-002; gap = 8.7e-001
>   5: obj =  2.898292874e+002; rpi = 3.4e-015; rdi = 7.7e-003; gap = 7.4e-001
>   6: obj =  1.503381835e+002; rpi = 1.4e-015; rdi = 4.6e-003; gap = 4.9e-001
>   7: obj =  8.660671850e+001; rpi = 2.1e-015; rdi = 5.6e-004; gap = 9.0e-002
>   8: obj =  7.976196926e+001; rpi = 1.3e-015; rdi = 5.6e-005; gap = 9.8e-003
>   9: obj =  7.907619834e+001; rpi = 1.6e-015; rdi = 5.6e-006; gap = 9.8e-004
>  10: obj =  7.900761984e+001; rpi = 2.1e-015; rdi = 5.6e-007; gap = 9.8e-005
>  11: obj =  7.900076198e+001; rpi = 1.9e-015; rdi = 5.6e-008; gap = 9.8e-006
>  12: obj =  7.900007620e+001; rpi = 2.5e-015; rdi = 5.6e-009; gap = 9.8e-007
>  13: obj =  7.900007572e+001; rpi = 1.5e-009; rdi = 5.6e-009; gap = 9.8e-007
>  14: obj =  7.900000757e+001; rpi = 1.5e-010; rdi = 5.6e-010; gap = 9.8e-008
>  15: obj =  7.900000076e+001; rpi = 1.5e-011; rdi = 5.6e-011; gap = 9.8e-009
> OPTIMAL SOLUTION FOUND
> Time used:   0.4 secs
> Memory used: 10.2 Mb (10737856 bytes)
> glp_write_ipt: writing interior-point solution to `temp_solved.txt'...
> 
> The console output when using the API is:
> 
> Running optimization...glp_write_lp: writing problem data to 
> `test_prob_100_lp.t
> xt'...
> Scaling...
>  A: min|aij| = 1.000e+000  max|aij| = 1.000e+000  ratio = 1.000e+000
> Problem data seem to be well scaled
> glp_interior: original LP problem has 7958 rows and 24014 columns
> glp_interior: transformed LP problem has 7958 rows and 24014 columns
> lpx_interior: A has 47748 non-zeros
> lpx_interior: S has 19825 non-zeros (upper triangle)
> lpx_interior: minimal degree ordering...
> lpx_interior: computing Cholesky factorization...
> lpx_interior: U has 93259 non-zeros
> lpx_interior: guessing initial point...
> Optimization begins...
>   0: obj =  1.887812891e+004; rpi = 9.7e-007; rdi = 2.7e+000; gap = 1.0e+000
>   1: obj =  1.115921387e+004; rpi = 8.8e-007; rdi = 2.7e-001; gap = 1.0e+000
>   2: obj =  2.881189941e+003; rpi = 8.4e-007; rdi = 4.2e-002; gap = 9.8e-001
>   3: obj =  1.001948669e+003; rpi = 7.7e-007; rdi = 2.0e-002; gap = 9.4e-001
>   4: obj =  5.424824829e+002; rpi = 1.4e-006; rdi = 1.1e-002; gap = 8.7e-001
>   5: obj =  2.898280334e+002; rpi = 2.7e-006; rdi = 7.7e-003; gap = 7.4e-001
>   6: obj =  1.503356628e+002; rpi = 1.2e-006; rdi = 4.6e-003; gap = 4.9e-001
>   7: obj =  8.660641479e+001; rpi = 2.1e-006; rdi = 5.6e-004; gap = 9.0e-002
>   8: obj =  7.976927185e+001; rpi = 2.0e-006; rdi = 5.6e-005; gap = 9.8e-003
>   9: obj =  7.908045197e+001; rpi = 9.7e-007; rdi = 5.6e-006; gap = 1.0e-003
>  10: obj =  7.899995422e+001; rpi = 5.5e-007; rdi = 5.7e-007; gap = 2.8e-006
>  11: obj =  7.899996948e+001; rpi = 6.6e-007; rdi = 1.2e-007; gap = 9.5e-008
>  12: obj =  7.900000763e+001; rpi = 5.1e-007; rdi = 1.0e-007; gap = 9.5e-008
>  13: obj =  7.900004578e+001; rpi = 5.5e-007; rdi = 1.0e-007; gap = 5.7e-007
>  14: obj =  7.900009155e+001; rpi = 3.3e-006; rdi = 9.9e-008; gap = 1.1e-006
> NUMERIC INSTABILITY; SEARCH TERMINATED
> The best point  7.900000763e+001 was reached on iteration 12
> 
> I used the 4.35 version on a win32 machine.
> 
> I also tried the 4.46 version but I get numeric instability in both cases.

Sorry, the glpk interior-point solver is not robust, and sometimes it
prematurely terminates the search due to numerical instability on
solving a Newtonian system. You might use the simplex solver, which is
much more robust.

To obtain identical results check options passed to the C compiler that
affect the floating-point precision used. For example, on Intel Pentium
glpsol might be compiled to use full 64-bit precision (gcc does this by
default) while your program may use only 53-bit precision.

BTW, I could successfully solved your lp with glpsol 4.46 on my Intel
Pentium PC:

GLPSOL: GLPK LP/MIP Solver, v4.46
Parameter(s) specified in the command line:
 --lp test_prob_100_lp.txt --interior
Reading problem data from `test_prob_100_lp.txt'...
7958 rows, 24014 columns, 47748 non-zeros
11009 lines were read
Scaling...
 A: min|aij| =  1.000e+00  max|aij| =  1.000e+00  ratio =  1.000e+00
Problem data seem to be well scaled
Original LP has 7958 row(s), 24014 column(s), and 47748 non-zero(s)
Working LP has 7958 row(s), 24014 column(s), and 47748 non-zero(s)
Matrix A has 47748 non-zeros
Matrix S = A*A' has 19825 non-zeros (upper triangle)
Approximate minimum degree ordering (AMD)...
Computing Cholesky factorization S = L*L'...
Matrix L has 87343 non-zeros
Guessing initial point...
Optimization begins...
  0: obj =   1.887813906e+04; rpi =  1.2e-15; rdi =  2.7e+00; gap =
1.0e-00
  1: obj =   1.115924070e+04; rpi =  8.0e-16; rdi =  2.7e-01; gap =
1.0e-00
  2: obj =   2.881199640e+03; rpi =  1.1e-15; rdi =  4.2e-02; gap =
9.8e-01
  3: obj =   1.001952442e+03; rpi =  1.5e-15; rdi =  2.0e-02; gap =
9.4e-01
  4: obj =   5.424831020e+02; rpi =  2.5e-15; rdi =  1.1e-02; gap =
8.7e-01
  5: obj =   2.898292874e+02; rpi =  9.4e-15; rdi =  7.7e-03; gap =
7.4e-01
  6: obj =   1.503381835e+02; rpi =  3.5e-15; rdi =  4.6e-03; gap =
4.9e-01
  7: obj =   8.660671850e+01; rpi =  2.0e-15; rdi =  5.6e-04; gap =
9.0e-02
  8: obj =   7.976196926e+01; rpi =  2.5e-15; rdi =  5.6e-05; gap =
9.8e-03
  9: obj =   7.907619834e+01; rpi =  5.7e-15; rdi =  5.6e-06; gap =
9.8e-04
 10: obj =   7.900761984e+01; rpi =  5.7e-15; rdi =  5.6e-07; gap =
9.8e-05
 11: obj =   7.900076198e+01; rpi =  3.3e-15; rdi =  5.6e-08; gap =
9.8e-06
 12: obj =   7.900007620e+01; rpi =  3.0e-15; rdi =  5.6e-09; gap =
9.8e-07
 13: obj =   7.900000762e+01; rpi =  2.2e-15; rdi =  5.6e-10; gap =
9.8e-08
 14: obj =   7.900000076e+01; rpi =  5.6e-15; rdi =  5.6e-11; gap =
9.8e-09
OPTIMAL SOLUTION FOUND
Time used:   1.0 secs
Memory used: 14.9 Mb (15593576 bytes)