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A derivative-free algorithm for spherically constrained optimization

Author

Listed:
  • Min Xi

    (Nanjing Normal University
    Guangdong University of Foreign Studies)

  • Wenyu Sun

    (Nanjing Normal University)

  • Yannan Chen

    (South China Normal University)

  • Hailin Sun

    (Nanjing Normal University)

Abstract

Spherically constrained optimization, which minimizes an objective function on a unit sphere, has wide applications in numerical multilinear algebra, signal processing, solid mechanics, etc. In this paper, we consider a certain case that the derivatives of the objective function are unavailable. This case arises frequently in computational science, chemistry, physics, and other enormous areas. To explore the spherical structure of the above problem, we apply the Cayley transform to preserve iterates on the sphere and propose a derivative-free algorithm, which employs a simple model-based trust-region framework. Under mild conditions, global convergence of the proposed algorithm is established. Preliminary numerical experiments illustrate the promising performances of our algorithm.

Suggested Citation

  • Min Xi & Wenyu Sun & Yannan Chen & Hailin Sun, 2020. "A derivative-free algorithm for spherically constrained optimization," Journal of Global Optimization, Springer, vol. 76(4), pages 841-861, April.
    • Handle: RePEc:spr:jglopt:v:76:y:2020:i:4:d:10.1007_s10898-020-00875-2
    DOI: 10.1007/s10898-020-00875-2
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    References listed on IDEAS

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    1. C.J. Price & I.D. Coope & D. Byatt, 2002. "A Convergent Variant of the Nelder–Mead Algorithm," Journal of Optimization Theory and Applications, Springer, vol. 113(1), pages 5-19, April.
    2. Wenyu Sun & Ya-Xiang Yuan, 2006. "Optimization Theory and Methods," Springer Optimization and Its Applications, Springer, number 978-0-387-24976-6, June.
    3. Genetha Anne Gray & Tamara G. Kolda & Ken Sale & Malin M. Young, 2004. "Optimizing an Empirical Scoring Function for Transmembrane Protein Structure Determination," INFORMS Journal on Computing, INFORMS, vol. 16(4), pages 406-418, November.
    4. Kazuo Yamaguchi, 2016. "Borda winner in facility location problems on sphere," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(4), pages 893-898, April.
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