SIAM Journal on Optimization, Volume 30, Issue 2, Page 1094-1118, January 2020.
Based on concepts like the $k$th convex hull and finer characterization of nonconvexity of a function, we propose a refinement of the Shapley--Folkman lemma and derive a new estimate for the duality gap of nonconvex optimization problems with separable objective functions. We apply our result to the network utility maximization problem in networking and the dynamic spectrum management problem in communication as examples to demonstrate that the new bound can be qualitatively tighter than the existing ones. The idea is also applicable to cases with general nonconvex constraints.

中文翻译：

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通过改进的Shapley-Folkman Lemma进行对偶间隙估计

SIAM优化杂志，第30卷，第2期，第1094-1118页，2020年1月。
基于第$ k $个凸包和函数非凸性的更精细表征等概念，我们提出了Shapley-Folkman引理的改进并得出具有可分离目标函数的非凸优化问题对偶间隙的新估计。我们将结果应用到网络中的网络效用最大化问题和通信中的动态频谱管理问题中，以举例说明新边界在质量上比现有边界更严格。这个想法也适用于具有一般非凸约束的情况。