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A DCA-Newton method for quartic minimization over the sphere

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Abstract

In this paper, a method for quartic minimization over the sphere is studied. It is based on an equivalent difference of convex (DC) reformulation of this problem in the matrix variable. This derivation also induces a global optimality certification for the quartic minimization over the sphere. An algorithm with the subproblem being solved by a semismooth Newton method is then proposed for solving the quartic minimization problem. The efficiency of this algorithm and the global optimality certification are illustrated by numerical experiments.

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Acknowledgements

The authors are grateful to the anonymous referees for their suggestions and comments on the manuscript.

Funding

This work is partially supported by the Natural Science Foundation of Zhejiang Province, China (Grant No. LY22A010022 and Grant No. LD19A010002), and the National Natural Science Foundation of China (Grant No. 11771328, Grant No. 12171128 and Grant No. 12171357).

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Authors and Affiliations

  1. Department of Mathematics, School of Science, Hangzhou Dianzi University, Hangzhou, 310018, China

    Shenglong Hu & Jinling Zhou

  2. School of Mathematics, Tianjin University, Tianjin, 300072, China

    Yong Wang

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  1. Shenglong Hu
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  2. Yong Wang
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  3. Jinling Zhou
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Correspondence to Yong Wang.

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Communicated by: Guoyin Li

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Hu, S., Wang, Y. & Zhou, J. A DCA-Newton method for quartic minimization over the sphere. Adv Comput Math 49, 53 (2023). https://doi.org/10.1007/s10444-023-10040-4

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