Suppose we have a primal problem P which is stated as a maximization problem max c T x.The dual problem is defined only for a primal minimization problem.Then what is the dual problem of P ?Is it implicit, that the dual problem of P is the dual problem of P stated as the minimization problem min − c T x ?Surely these two primal problems are equivalent in the sense that their optimal solution x ¯ are equal (if it exist). However, the objective values are the same only if we ignore the sign !

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Suppose we have a primal problem   P which is stated as a maximization problem   max      c          T        x.The dual problem is defined only for a primal minimization problem.Then what is the dual problem of   P ?Is it implicit, that the dual problem of   P is the dual problem of   P stated as the minimization problem   min  −      c    T    x ?Surely these two primal problems are equivalent in the sense that their optimal solution             x      ¯       are equal (if it exist). However, the objective values are the same only if we ignore the sign !

Ronnie Glenn · Accepted Answer

I do not have the book of Bertsimas in front of me, but it should state somewhere that &quot;the dual of the dual is again the primal&quot;.So, concerning your question the dual of a max problem is a min problem without any need to transform the max firstly to a min and then take the dual.If you insist transforming first to a min problem and then taking the dual, then it is correct (as you say) that  max      c    T    x  =  −  min  (  −      c    T    )  xso the objective value will be the same but with opposite signs.

Suppose we have a primal problem P which is stated as a maximization problem <mo movableli

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