Turnpike Theorems for Integer Programming Problems

Cover Turnpike Theorems for Integer Programming Problems
Turnpike Theorems for Integer Programming Problems
Jeremy F Shapiro
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COROLLARY 1: Given a chain u = {b } t h ^ K, where v=l ^ E t . E. + V Z t 1 E I 1 e I for given non-negative integers t. , i e I, there exists a v such that for all + V >_ v G(A; t. , 1 £ l'^) = C(b^).
Proof: This corollary can be proven either directly or by using lemma 3.
We give the direct proof. Solve (9) for G(A; t. , i e I ) Thereby obtaining * + the optimal correction x . Then choose v large enough so that the constraints " - * + I V.. X. v . J=l iJ J - ^ LEMMA 4: Given any set I CT {l,
... ... , m}, there exist non-negative integers ** - ** u. , i e 1, such that for all b e IC satisfying b. > u. , i e I, 1 D 1 — 1 G(

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