Location of a conservative hyperplane for cutting plane methods in disjoint bilinear programming

  • Xi Chen
  • Ji-hong Zhang
  • Xiao-song DingEmail author
  • Tian Yang
  • Jing-yi Qian
Original paper


Although several classes of cutting plane methods for deterministically solving disjoint bilinear programming (DBLP) have been proposed, the frequently encountered computational issue regarding the generation of a suitable cut from a degenerate vertex in a pseudo-global minimizer (PGM) still remains. Among the approaches to dealing with degeneracy, the most recent one is to generate a conservative cut. Nevertheless, the computational performance of the corresponding distance-following algorithm for its location seems far from satisfactory. This paper proposes several approaches that can be utilized to efficiently locate a conservative hyperplane from a degenerate vertex in a PGM. Extensive experiments are conducted to evaluate their performance from the dimensionality as well as the degree of degeneracy. From the computational viewpoint, these new approaches can outperform the earlier developed distance-following algorithm, and thereby can be incorporated into cutting plane methods for solving DBLP.


Cutting plane method Degeneracy removal Conservative cut 



The authors are grateful to the editor and the anonymous referee for their insightful comments to significantly improve this paper.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Xi Chen
    • 1
  • Ji-hong Zhang
    • 1
  • Xiao-song Ding
    • 1
    Email author
  • Tian Yang
    • 2
  • Jing-yi Qian
    • 3
  1. 1.International Business SchoolBeijing Foreign Studies UniversityBeijingPeople’s Republic of China
  2. 2.School of Computer Science and TechnologyBeijing Institute of TechnologyBeijingPeople’s Republic of China
  3. 3.High School Affiliated to Shanghai Jiao Tong UniversityShanghaiPeople’s Republic of China

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