[Help-glpk] Pricing with dual values

[Matteo Fortini]

Hi,
I'm implementing a B&C algorithm for the TSP, and I'm using pricing in 
order to avoid inserting edges in the LP which are not needed.
I'm thus using get_row_dual() in order to compute the reduced costs of 
the variables.
My first question is: what sign is the value returned by get_row_dual 
(), i.e. is the auxiliary variable for a constraint introduced always 
with a + sign, or it depends on the sense of the constraint? Moreover, 
are auxiliary variables introduced even for EQ constraints?
This is to know if the reduced cost of a variable not in the LP has to 
be computed as
{\bar c_j} = c_j - u^T Aj
or
{\bar c_j} = c_j + u^T Aj
where u is the vector of all the values returned by get_row_dual ()

My second question regards the case in which the LP is INFEASIBLE. Can I 
use the row duals in order to find the variables which need to be 
included in the LP in order to get it feasible again, i.e. does 
lpx_simplex put in the rows' duals the values for the first phase of the 
primal simplex? I turned off the presolver and the dual opt...
If this is not the case, is there any other method I could use to find 
which variables are needed to form the initial basis?

Thank you very much,
Matteo