Continuous submodularity: Non-convex structure with guaranteed optimization

Recently, we are working on optimizing a class of non-convex objectives with a celebrated and general structure, called continuous submodularity. People know that submodularity is a classical structure in combinatorial optimization, it turns out that continuous submodularity is also a common non-convex structure for many continuous objectives, with strong guarantees for both minimization and maximization.
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