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Minimizing Ratio of Monotone Non-submodular Functions

  • Yi-Jing Wang
  • Da-Chuan Xu
  • Yan-Jun Jiang
  • Dong-Mei ZhangEmail author
Article
  • 35 Downloads

Abstract

In this paper, we investigate the problem of minimizing the ratio of normalized non-negative monotone non-submodular set function f and normalized non-negative monotone set function g. We take advantage of the greedy technique and get a performance guarantee depending on the generalized curvature and inverse generalized curvature of f, as well as the submodularity ratio of g. Our results generalize the works of Bai et al. (Algorithms for optimizing the ratio of submodular functions. In: Proceedings of the 33rd International Conference on Machine Learning, 2016) and Qian et al. (Optimizing ratio of monotone set functions. In: Proceedings of the 26th International Joint Conference on Artificial Intelligence, 2017).

Keywords

Non-submodular Set functions Minimizing ratio Greedy algorithm 

Mathematics Subject Classification

90C27 68W25 

Notes

Acknowledgements

We appreciate the anonymous reviewers for their helpful comments on the earlier draft of this paper.

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Copyright information

© Operations Research Society of China, Periodicals Agency of Shanghai University, Science Press, and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Yi-Jing Wang
    • 1
  • Da-Chuan Xu
    • 1
  • Yan-Jun Jiang
    • 1
    • 2
  • Dong-Mei Zhang
    • 3
    Email author
  1. 1.Department of Information and Operations Research, College of Applied SciencesBeijing University of TechnologyBeijingChina
  2. 2.School of Mathematics and Statistics ScienceLudong UniversityYantaiChina
  3. 3.School of Computer Science and TechnologyShandong Jianzhu UniversityJinanChina

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