[Scip] why the dual solution is non-positive?

[XiangyongLi]

Dear all,

For my B&P, I have some problem: 

SCIP returned non-positive dual solution for all constraints.  These dual solutions logically should be non-negative. 


My problem is a minimization model with some equalities and some "<=" constraints. 

min f(x)

s.t.
Ax=b    (1)
Cx<=d  (2)
x is binary

Logically I know that the dual solutions of constraints (2) are non-negative. In SCIP, we should create initial constraints using format "lhs <= .... <= rhs" for either minimization or maximization problem. In my code SCIPgetDualsolLinear() returns non-positive dual solutions of constraints (2).


For minimization problem, can I say SCIP returns the dual solutions of constraints for a standard formulation (say all constraints are ">=") ?  Concerning my problem, the dual solution of each equality constraint is the same as the one SCIP returns.  But for inequality constraints, the dual solutions should be negative of values that SCIP returns. 


Is the above argument is correct?  Thanks.

Best regards.


Xiangyong Li
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