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[Help-glpk] Many basic vars = 0, many non-basic are on upper-bound

From: Joey Rios
Subject: [Help-glpk] Many basic vars = 0, many non-basic are on upper-bound
Date: Thu, 11 Jun 2009 19:26:05 -0700

My decision variables are all binary.  During the solve process (for the relaxation) many of the basic variables have a value of 0.0.  This implies degeneracy, which I feel somewhat comfortable with.  At the same time, many of my non-basic variables return GLP_NU (non-basic variable on its upper bound, i.e. primal value is 1) when I try glp_get_col_stat().  I'm trying to get a better understanding of what this means.

Nothing in my model is broken and the GLPK chugs along and provides the correct answer, so I guess I'm just asking for a little clarification on what "non-basic on its upper bound" means in terms of the simplex algorithm. 

My variables are often part of a convex combination, so the sum of some subset of them needs to be 1.  It seems odd that one of them from this subset would be basic with a value of zero and another is non-basic with a value of 1.  I'm trying to understand what algorithmic paths might be taken to get to such a solution.

I know the question is a tad vague, but any insight is appreciated.


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