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Unconstrained minimization of block-circulant polynomials via semidefinite program in third-order tensor space

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Abstract

In this paper, unconstrained minimization with block-circulant structured polynomials is studied. A specifically designed method is presented to show that it can solve problems with sizes much larger than the classical Lasserre’s semidefinite relaxation. The proposed approach is in the same spirit of Lasserre’s relaxation but with a careful exploration of the underlying circulant structure, which helps reducing the sizes of the result semidefinite program problems significantly. Despite of the reduction, a certification for the global optimality is derived as well.

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Authors and Affiliations

  1. Department of Mathematics, National University of Defense Technology, Changsha, 410073, Hunan, People’s Republic of China

    Meng-Meng Zheng

  2. School of Mathematics, Tianjin University, Tianjin, 300350, People’s Republic of China

    Zheng-Hai Huang

  3. Department of Mathematics, School of Science, Hangzhou Dianzi University, Hangzhou, 310018, People’s Republic of China

    Sheng-Long Hu

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  1. Meng-Meng Zheng
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  2. Zheng-Hai Huang
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Correspondence to Zheng-Hai Huang.

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This work was partially supported by the National Natural Science Foundation of China (Grant Nos. 11871051 and 12171128), the Natural Science Foundation of Zhejiang Province, China (Grant Nos. LD19A010002 and LY22A010022) and China Postdoctoral Science Foundation (Grant No 2021MD703978).

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Zheng, MM., Huang, ZH. & Hu, SL. Unconstrained minimization of block-circulant polynomials via semidefinite program in third-order tensor space. J Glob Optim 84, 415–440 (2022). https://doi.org/10.1007/s10898-022-01148-w

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  • DOI: https://doi.org/10.1007/s10898-022-01148-w

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