Unconstrained minimization of block-circulant polynomials via semidefinite program in third-order tensor space
Meng-Meng Zheng (),
Zheng-Hai Huang () and
Sheng-Long Hu ()
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Meng-Meng Zheng: National University of Defense Technology
Zheng-Hai Huang: Tianjin University
Sheng-Long Hu: Hangzhou Dianzi University
Journal of Global Optimization, 2022, vol. 84, issue 2, No 7, 415-440
Abstract:
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.
Keywords: Unconstrained polynomial optimization problem; Block-circulant structure; Lasserre’s relaxation; Semidefinite program; 65K05; 90C22 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10898-022-01148-w
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