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Maximizing a non-decreasing non-submodular function subject to various types of constraints

Author

Listed:
  • Cheng Lu

    (University of Chinese Academy of Sciences)

  • Wenguo Yang

    (University of Chinese Academy of Sciences)

  • Ruiqi Yang

    (University of Chinese Academy of Sciences)

  • Suixiang Gao

    (University of Chinese Academy of Sciences)

Abstract

In this paper, we firstly study the problem of maximizing a $$\gamma $$ γ -weakly DR-submodular function under a general matroid constraint. We present a local search algorithm, which is guided by a tailored potential function, for solving this problem. We prove that our algorithm produces a ( $$1 - e^{-\gamma } - \epsilon $$ 1 - e - γ - ϵ )-approximate solution. To the best of our knowledge, it’s the first algorithm achieving the tight approximation guarantee for such maximization problem. In addition, we study the maximization of the sum of submodular and supermodular functions. We show that this problem can be reduced to the maximization of submodular and linear sums. Based on this reduction, we derive new and improved approximation bounds for the problem under various types of constraints.

Suggested Citation

  • Cheng Lu & Wenguo Yang & Ruiqi Yang & Suixiang Gao, 2022. "Maximizing a non-decreasing non-submodular function subject to various types of constraints," Journal of Global Optimization, Springer, vol. 83(4), pages 727-751, August.
    • Handle: RePEc:spr:jglopt:v:83:y:2022:i:4:d:10.1007_s10898-021-01123-x
    DOI: 10.1007/s10898-021-01123-x
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    References listed on IDEAS

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    1. Fisher, M.L. & Nemhauser, G.L. & Wolsey, L.A., 1978. "An analysis of approximations for maximizing submodular set functions - 1," LIDAM Reprints CORE 334, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    7. Maxim Sviridenko & Jan Vondrák & Justin Ward, 2017. "Optimal Approximation for Submodular and Supermodular Optimization with Bounded Curvature," Mathematics of Operations Research, INFORMS, vol. 42(4), pages 1197-1218, November.
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