# Refined Shapely-Folkman Lemma and Its Application in Duality Gap Estimation

@article{Bi2016RefinedSL, title={Refined Shapely-Folkman Lemma and Its Application in Duality Gap Estimation}, author={Yingjie Bi and Ao Tang}, journal={arXiv: Optimization and Control}, year={2016} }

Based on concepts like kth 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 a network flow problem and the dynamic spectrum management problem in communication systems as examples to demonstrate that the new bound can be qualitatively tighter than the existing ones. The idea is also…

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