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A Tensor Optimization Algorithm for Computing Lagrangians of Hypergraphs

Author

Listed:
  • Jingya Chang

    (Guangdong University of Technology)

  • Bin Xiao

    (Guangdong University of Technology)

  • Xin Zhang

    (Suqian University)

Abstract

The Lagrangian of a hypergraph is a crucial tool for studying hypergraph extremal problems. Though Lagrangians of some special structure hypergraphs, such as complete uniform hypergraphs or three order uniform hypergraphs, have closed-form solutions, it is a challenging problem to compute the Lagrangian of a general large scale hypergraph. In this paper, we exploit a fast computational scheme involving the adjacency tensor of a hypergraph. Furthermore, we propose to utilize the gradient projection method on a simplex from nonlinear optimization for solving the Lagrangian of a large-scale hypergraph iteratively. Using the Łojasiewicz gradient inequality, we analyze the global and local convergence of the gradient projection method. Numerical experiments illustrate that the proposed numerical method could compute Lagrangians of large-scale hypergraphs efficiently.

Suggested Citation

  • Jingya Chang & Bin Xiao & Xin Zhang, 2023. "A Tensor Optimization Algorithm for Computing Lagrangians of Hypergraphs," Journal of Optimization Theory and Applications, Springer, vol. 198(2), pages 588-604, August.
    • Handle: RePEc:spr:joptap:v:198:y:2023:i:2:d:10.1007_s10957-023-02215-2
    DOI: 10.1007/s10957-023-02215-2
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    References listed on IDEAS

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    1. Hédy Attouch & Jérôme Bolte & Patrick Redont & Antoine Soubeyran, 2010. "Proximal Alternating Minimization and Projection Methods for Nonconvex Problems: An Approach Based on the Kurdyka-Łojasiewicz Inequality," Mathematics of Operations Research, INFORMS, vol. 35(2), pages 438-457, May.
    2. Yanping Sun & Qingsong Tang & Cheng Zhao & Yuejian Peng, 2014. "On the Largest Graph-Lagrangian of 3-Graphs with Fixed Number of Edges," Journal of Optimization Theory and Applications, Springer, vol. 163(1), pages 57-79, October.
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