[Help-glpk] Characterizing multiple solutions

[Chris Smith]

Hi everyone,

I'm currently using GLPK to solve a basic LP problem (about 5000 structural
variables and 4000 constraints).  Of those 5000 variables, about 4000 (same
number as there are constraints) are error terms which provide slack for the
constraints themselves, and are then minimized in the objective function.  The
remaining 1000 are the ones whose final values I actually care about.  Because
those remaining 1000 are only limited by their variable bounds and a few
inequality constraints, and are not actually in the objective function, they
can often vary widely without changing the objective function at all.

So here's the problem: I'd basically like to answer the (vaguely stated)
question: what point (set of values for all the variables) is at the "center"
of the space of optimal solutions to this problem?  I understand there will
probably be different definitions possible for the word "center" there, and
I'd like to hear what definitions of "center" will be possible to discover.

Any ideas?

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