Duality

S. Vajda
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S. Vajda: University of Sussex

Chapter Chapter 3 in Linear Programming, 1981, pp 50-64 from Springer

Abstract: Abstract As a counterpart, or obverse, of a problem: maximize b′x, subject to $$ Ax \leqslant c,{\text{ }}x{\text{ }} \geqslant 0 $$ (P) consider its ‘dual’: minimize c′y, subject to $$ A\prime y{\text{ }} \geqslant {\text{ }}b,{\text{ }}y{\text{ }} \geqslant 0 $$ (D) The original, ‘primal’ problem, has m inequality constraints, in n variables, while the ‘dual’ problem has n inequality constraints and m variables. Also, in the problem to be maximized the left hand side must not exceed the right hand side, while in that to be minimized, the left hand side is not smaller than the right hand side. In either problem, though, the variables are restricted to having non-negative values.

Date: 1981
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DOI: 10.1007/978-94-011-6924-0_3

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