Assume a linear minimization problem.

The dual value of an inequality constraint eg '<' or '>' is the marginal improvement in the objective function (ie marginal reduction) from marginally increasing the right-hand-side of the constraint.
However, what is the dual value of an equality constraint ?

asked 17 Jul '14, 10:33

spyimp's gravatar image

accept rate: 0%

I assume you mean '<=' and '>=' constraints (we don't really like strict inequalities around here).

The same logic applies for equality constraints. You can think of an equality constraint as two inequalities, thus depending on the sign of the dual value the constraint is either tight (improvement possible in that direction) from above or tight from below.

Be careful with signs in this setting. Minimization or maximization can confuse things and also whether you are dealing with dual solutions or reduced cost of slacks (which are the negative of the dual solution).


answered 17 Jul '14, 11:44

Philipp%20Christophel's gravatar image

Philipp Chri...
accept rate: 22%

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Asked: 17 Jul '14, 10:33

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Last updated: 17 Jul '14, 11:44

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