[Scip] why dual solutions of Soplex are different from CPLEX

[Marco Luebbecke]

Hi XiangyongLi,

lixiangyong> Dear all, I use SCIP to develop a branch and price method
lixiangyong> where soplex is used as the LP solver.  At the root node,
lixiangyong> I use SCIPgetDualsolLinear to get dual solutions. In the
lixiangyong> mean while, I also output the corresponding MIP at this
lixiangyong> node. I use CPLEX to solve the corresponding LP and get
lixiangyong> dual solutions.  But these dual solutions are different
lixiangyong> from those obtained by SCIPgetDualsolLinear in my B&P.


as long as the dual objective function value is identical I would see
no troubles. There may be more than one dual optimal solution, and
using a simplex type algorithm to solve the LP relaxation you end up
in an optimal basic solution more or less "randomly" chosen.

Does this make sense?

--Marco