A Generalized Programming Algorithm for Integer Programming Problems With Many C

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A Generalized Programming Algorithm for Integer Programming Problems With Many C
Jeremy F Shapiro
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, m (13b) j=m+l '^ ^ ' ^^ n I j=m+l I a. X. = & - \^ mod (qi, ... , q^) ('13c) X. Non-negative integer, j=m+l, ... , n (13d) The cost z* in (13) is the minimal cost of using activity a^ at least once. We prove the lemma by showing that 13 W-, A. - j_ r-/n I . R. J\ ~->L z* 1 c^ + u a^^ + ig + G(e-A^; u^) - G^b (14) The right hand side of this inequality is by assumption at least as great as the upper bound z on the optimal cost of (1), and thus if (14) holds we can conclude that the activity a ...can be (jeieted.
' The minimal cost of problem (13) with che constraints (13b) ignored . Q + (T + G(b-Xj^; u^). The case A^= - ^ -S is Zn + c + G(b-x ; u ). The case A„= 1 in oroblem (13), and the lower bound j=m+l ^ G(0; u ) is correct.


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