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Gradient projection method on the sphere, complementarity problems and copositivity

Author

Listed:
  • Orizon Pereira Ferreira

    (IME/UFG)

  • Yingchao Gao

    (University of Birmingham)

  • Sándor Zoltán Németh

    (University of Birmingham)

  • Petra Renáta Rigó

    (Corvinus University of Budapest)

Abstract

By using a constant step-size, the convergence analysis of the gradient projection method on the sphere is presented for a closed spherically convex set. This algorithm is applied to discuss copositivity of operators with respect to cones. This approach can also be used to analyse solvability of nonlinear cone-complementarity problems. To our best knowledge this is the first numerical method related to the copositivity of operators with respect to the positive semidefinite cone. Numerical results concerning the copositivity of operators are also provided.

Suggested Citation

  • Orizon Pereira Ferreira & Yingchao Gao & Sándor Zoltán Németh & Petra Renáta Rigó, 2024. "Gradient projection method on the sphere, complementarity problems and copositivity," Journal of Global Optimization, Springer, vol. 90(1), pages 1-25, September.
    • Handle: RePEc:spr:jglopt:v:90:y:2024:i:1:d:10.1007_s10898-024-01390-4
    DOI: 10.1007/s10898-024-01390-4
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    References listed on IDEAS

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    1. Bomze, Immanuel M., 2012. "Copositive optimization – Recent developments and applications," European Journal of Operational Research, Elsevier, vol. 216(3), pages 509-520.
    2. Hiroyuki Sato, 2023. "Riemannian optimization on unit sphere with p-norm and its applications," Computational Optimization and Applications, Springer, vol. 85(3), pages 897-935, July.
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    4. Julia Sponsel & Stefan Bundfuss & Mirjam Dür, 2012. "An improved algorithm to test copositivity," Journal of Global Optimization, Springer, vol. 52(3), pages 537-551, March.
    5. Sándor Zoltán Németh & George Isac, 2008. "Scalar and Asymptotic Scalar Derivatives," Springer Optimization and Its Applications, Springer, number 978-0-387-73988-5, December.
    6. Carmo Brás & Gabriele Eichfelder & Joaquim Júdice, 2016. "Copositivity tests based on the linear complementarity problem," Computational Optimization and Applications, Springer, vol. 63(2), pages 461-493, March.
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