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Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 319))


In mathematical programming duality means that corresponding to every optimization (say minimization) problem, one relates a maximization problem in such a manner that by solving the latter problem it is possible to get the optimal value of the first one. To see the crucial ideas of this method let us consider a linear mathematical programming problem, denoted by (LP):

$$ \begin{gathered} \min {\kern 1pt} {\kern 1pt} cx \hfill \\ s.t.{\kern 1pt} x \in {R^{n}},{\kern 1pt} Ax \geqslant b \hfill \\ \end{gathered} $$

, where cRn, bRm and A is an (n × m)-matrix.

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© 1989 Springer-Verlag Berlin Heidelberg

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Luc, D.T. (1989). Duality. In: Theory of Vector Optimization. Lecture Notes in Economics and Mathematical Systems, vol 319. Springer, Berlin, Heidelberg.

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50541-9

  • Online ISBN: 978-3-642-50280-4

  • eBook Packages: Springer Book Archive

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