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On the maxima of motzkin-straus programs and cliques of graphs

Author

Listed:
  • Qingsong Tang

    (Northeastern University)

  • Xiangde Zhang

    (Northeastern University)

  • Cheng Zhao

    (Shandong University
    Indiana State University)

  • Peng Zhao

    (Indiana State University)

Abstract

In this paper, we establish a connection between the local maximizers (global maximizers) of a Motzkin-Straus quadratic program and a specific type of regular multipartite cliques. Our work extends a remarkable connection between the maximum cliques and the global maximizers of the Motzkin-Straus quadratic program. This connection and its extensions can be successfully employed in optimization to provide heuristics for the maximal cliques in graphs. We provide two counterexamples to the results from previous work about the global and local maximizers of the Motzkin-Straus quadratic program. We then amend the previous theorems by introducing a new structure. We also answer two questions raised by Pelillo and Jagota about the maxima of the Motzkin-Straus quadratic program.

Suggested Citation

  • Qingsong Tang & Xiangde Zhang & Cheng Zhao & Peng Zhao, 2022. "On the maxima of motzkin-straus programs and cliques of graphs," Journal of Global Optimization, Springer, vol. 84(4), pages 989-1003, December.
    • Handle: RePEc:spr:jglopt:v:84:y:2022:i:4:d:10.1007_s10898-022-01187-3
    DOI: 10.1007/s10898-022-01187-3
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    References listed on IDEAS

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    1. Luana E. Gibbons & Donald W. Hearn & Panos M. Pardalos & Motakuri V. Ramana, 1997. "Continuous Characterizations of the Maximum Clique Problem," Mathematics of Operations Research, INFORMS, vol. 22(3), pages 754-768, August.
    2. David G. Luenberger & Yinyu Ye, 2008. "Linear and Nonlinear Programming," International Series in Operations Research and Management Science, Springer, edition 0, number 978-0-387-74503-9, December.
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