Numerical Issues Markowitz tolerance

[Simon]

Hi we are having a large LP Problem and having trouble with numerical issues.

Specifically with the automatic increase of markowitz tolerance. We created the problem in python with pyomo. 

I have to admit we did not care too much about coefficients and "smart" modelling etc. 

Objective range and RHS coefficient range seem pretty big, is it worth trying to reduce this range?

Is it possible to get information from the problem to identify problematic elements in the matrix? (e.g. the RHS values in the lp-file)

Thanks! 

Gurobi 6.5.0 (linux64) logging started Tue Apr 26 11:11:26 2016

Read LP format model from file /tmp/tmpvpdfnolu.pyomo.lp
Reading time = 32.26 seconds
(null): 3714269 rows, 8943816 columns, 16205711 nonzeros
Changed value of parameter QCPDual to 1
Prev: 0 Min: 0 Max: 1 Default: 0
Optimize a model with 3714269 rows, 8943816 columns and 16205711 nonzeros
Coefficient statistics:
Matrix range [3e-01, 2e+00]
Objective range [5e-01, 1e+11]
Bounds range [4e-02, 1e+05]
RHS range [3e-02, 2e+07]

Concurrent LP optimizer: primal simplex, dual simplex, and barrier
Showing barrier log only...

Presolve removed 0 rows and 0 columns (presolve time = 8s) ...
Presolve removed 895085 rows and 1937769 columns (presolve time = 10s) ...
Presolve removed 1009139 rows and 1937771 columns (presolve time = 17s) ...
Presolve removed 1009139 rows and 2035200 columns (presolve time = 26s) ...
Presolve removed 2287319 rows and 3313380 columns (presolve time = 38s) ...
Presolve removed 2287319 rows and 3314772 columns (presolve time = 40s) ...
Presolve removed 2287320 rows and 3323605 columns (presolve time = 45s) ...
Presolve removed 2287321 rows and 3336650 columns
Presolve time: 57.75s
Presolved: 1426948 rows, 5607166 columns, 10299295 nonzeros

Elapsed ordering time = 9s
Elapsed ordering time = 11s
Elapsed ordering time = 15s
Elapsed ordering time = 20s
Elapsed ordering time = 25s
Ordering time: 73.00s

Barrier statistics:
AA' NZ : 3.055e+06
Factor NZ : 8.491e+07 (roughly 3.5 GBytes of memory)
Factor Ops : 2.826e+10 (roughly 2 seconds per iteration)
Threads : 6

....

Followed by a lot of iterations

[Tobias Achterberg]

Small values in the objective, rhs, and bounds do not matter much, but big
values (in particular the 1e+11 objective coefficients) can hurt numerics.

For the matrix coefficients both, big and small values, are troublesome.

Tobias