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Concave Roofs and Downward Recovery for DR-Submodular Polynomial Maximization
We give approximation algorithms for $\max\{F(x):x\in\K\}$, where $\K$ is a nonempty compact down-closed convex subset of the unit cube and $F$ is a nonnegative diminishing-returns (DR) submodular polynomial: every entry of its Hessian is nonpositive on the cube. Starting from quadratic or cubic c
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