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Degeneracy removal in cutting plane methods for disjoint bilinear programming

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Abstract

Disjoint bilinear programming has appeared in miscellaneous practical applications. Although deterministic approaches such as cutting plane methods for solving it have been proposed, the frequently encountered computational problem regarding degeneracy still remains. This paper proposes a distance-following approach in order to generate a conservative hyperplane from a degenerate local star minimizer located by the augmented mountain climbing procedure, cut off it, and thus enable a cutting plane method to proceed without too much additional computational workload.

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Acknowledgments

The authors are grateful to two anonymous referees for their insightful comments to significantly improve this paper. The work was partially supported by Young Faculty Research Fund of BFSU (2015JT005), YETP (YETP0851), NSFC (71371032), Key Project of BFSU Research Programs (2011XG003), the Humanities and Social Science Research Project of Ministry of Education (13YJA630125), and the Fundamental Research Funds for the Central Universities.

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Authors and Affiliations

  1. International Business School, Beijing Foreign Studies University, Beijing, 100089, China

    Ji-hong Zhang & Xiao-song Ding

  2. Tippie College of Business, The University of Iowa, Iowa City, Iowa, 52242-1994, USA

    Xi Chen

  3. DECIDE, Department of Computer and Systems Sciences, Stockholm University, Forum 100, 164 40, Kista, Sweden

    Xiao-song Ding

Authors
  1. Ji-hong Zhang
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  2. Xi Chen
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  3. Xiao-song Ding
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Correspondence to Xiao-song Ding.

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Zhang, Jh., Chen, X. & Ding, Xs. Degeneracy removal in cutting plane methods for disjoint bilinear programming. Optim Lett 11, 483–495 (2017). https://doi.org/10.1007/s11590-016-1016-6

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