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Spectral projected gradient methods for generalized tensor eigenvalue complementarity problems

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Abstract

This paper looks at the tensor eigenvalue complementarity problem (TEiCP) which arises from the stability analysis of finite dimensional mechanical systems and is closely related to the optimality conditions for polynomial optimization. We investigate two monotone ascent spectral projected gradient (SPG) methods for TEiCP. We also present a shifted scaling-and-projection algorithm (SPA), which is a great improvement of the original SPA method proposed by Ling et al. (Comput. Optim. Appl. 63, 143–168 2016). Numerical comparisons with some existing gradient methods in the literature are reported to illustrate the efficiency of the proposed methods.

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Acknowledgements

The authors would like to thank two anonymous referees who have contributed to improve the quality of the paper.

Funding

This work was supported in part by the National Natural Science Foundation of China (No. 11571095, 11501100, 11661007), Program for Innovative Research Team in University of Henan Province (14IRTSTHN023).

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Authors and Affiliations

  1. Department of Mathematics, School of Science, Hangzhou Dianzi University, Hangzhou, China

    Gaohang Yu

  2. School of Mathematics and Information Science, Henan Normal University, Xinxiang County, China

    Yisheng Song

  3. Henan Engineering Laboratory for Big Data Statistical Analysis and Optimal Control, Henan Normal University, Xinxiang County, China

    Yisheng Song

  4. Department of Mathematics, Southeast University, Nanjing, China

    Yi Xu

  5. School of Mathematics and Computer Sciences, Gannan Normal University, Ganzhou, China

    Zefeng Yu

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  1. Gaohang Yu
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  2. Yisheng Song
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  3. Yi Xu
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  4. Zefeng Yu
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Correspondence to Gaohang Yu.

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Yu, G., Song, Y., Xu, Y. et al. Spectral projected gradient methods for generalized tensor eigenvalue complementarity problems. Numer Algor 80, 1181–1201 (2019). https://doi.org/10.1007/s11075-018-0522-2

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