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Value Functions of Separable Convex Integer Programs are Periodically Convex
We consider the periodic behavior of value functions $b\mapsto\min\{f(x)\ \vert\ Ax=b,\,x\in\mathbb Z_{\ge0}^n\}$ of integer programs. We show that there exists a positive integer $M$ depending only on the constraint matrix $A\in\mathbb Z^{m\times n}$ so that the value function is convex extensible
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