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

Anis Fradi (), Chafik Samir () and Ines Adouani ()
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Anis Fradi: Geostat Team, INRIA Bordeaux Sud-Ouest
Chafik Samir: University of Clermont Auvergne, LIMOS CNRS (UMR 6158)
Ines Adouani: University of Sousse

Journal of Optimization Theory and Applications, 2024, vol. 202, issue 3, No 4, 1077-1100

Abstract: 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.

Keywords: Riemannian optimization; Bayesian optimization; Spherical HMC; Parametrized surfaces; Spherical Gaussian processes; 62G05; 62G07; 60G15; 46F25; 46T30 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10957-024-02473-8

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