# A Reduction for Optimizing Lattice Submodular Functions with Diminishing Returns

27 Jun 2016

A function $f: \mathbb{Z}_+^E \rightarrow \mathbb{R}_+$ is DR-submodular if it satisfies $f({\bf x} + \chi_i) -f ({\bf x}) \ge f({\bf y} + \chi_i) - f({\bf y})$ for all ${\bf x}\le {\bf y}, i\in E$. Recently, the problem of maximizing a DR-submodular function $f: \mathbb{Z}_+^E \rightarrow \mathbb{R}_+$ subject to a budget constraint $\|{\bf x}\|_1 \leq B$ as well as additional constraints has received significant attention \cite{SKIK14,SY15,MYK15,SY16}... (read more)

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