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A New Bayesian Approach to Global Optimization on Parametrized Surfaces in $$\mathbb {R}^{3}$$ R 3

Author

Listed:
  • Anis Fradi

    (Geostat Team, INRIA Bordeaux Sud-Ouest)

  • Chafik Samir

    (University of Clermont Auvergne, LIMOS CNRS (UMR 6158))

  • Ines Adouani

    (University of Sousse)

Abstract

This work introduces a new Riemannian optimization method for registering open parameterized surfaces with a constrained global optimization approach. The proposed formulation leads to a rigorous theoretic foundation and guarantees the existence and the uniqueness of a global solution. We also propose a new Bayesian clustering approach where local distributions of surfaces are modeled with spherical Gaussian processes. The maximization of the posterior density is performed with Hamiltonian dynamics which provide a natural and computationally efficient spherical Hamiltonian Monte Carlo sampling. Experimental results demonstrate the efficiency of the proposed method.

Suggested Citation

  • Anis Fradi & Chafik Samir & Ines Adouani, 2024. "A New Bayesian Approach to Global Optimization on Parametrized Surfaces in $$\mathbb {R}^{3}$$ R 3," Journal of Optimization Theory and Applications, Springer, vol. 202(3), pages 1077-1100, September.
    • Handle: RePEc:spr:joptap:v:202:y:2024:i:3:d:10.1007_s10957-024-02473-8
    DOI: 10.1007/s10957-024-02473-8
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    References listed on IDEAS

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    1. Pooriya Beyhaghi & Ryan Alimo & Thomas Bewley, 2020. "A derivative-free optimization algorithm for the efficient minimization of functions obtained via statistical averaging," Computational Optimization and Applications, Springer, vol. 76(1), pages 1-31, May.
    2. C. Bruni & R. Bruni & A. De Santis & D. Iacoviello & G. Koch, 2002. "Global Optimal Image Reconstruction from Blurred Noisy Data by a Bayesian Approach," Journal of Optimization Theory and Applications, Springer, vol. 115(1), pages 67-96, October.
    3. Yaroslav D. Sergeyev & Marat S. Mukhametzhanov & Dmitri E. Kvasov & Daniela Lera, 2016. "Derivative-Free Local Tuning and Local Improvement Techniques Embedded in the Univariate Global Optimization," Journal of Optimization Theory and Applications, Springer, vol. 171(1), pages 186-208, October.
    4. Ines Adouani & Chafik Samir, 2020. "A Constructive Approximation of Interpolating Bézier Curves on Riemannian Symmetric Spaces," Journal of Optimization Theory and Applications, Springer, vol. 187(1), pages 158-180, October.
    5. Antanas Žilinskas & James Calvin, 2019. "Bi-objective decision making in global optimization based on statistical models," Journal of Global Optimization, Springer, vol. 74(4), pages 599-609, August.
    6. W. R. Gilks & P. Wild, 1992. "Adaptive Rejection Sampling for Gibbs Sampling," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 41(2), pages 337-348, June.
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