A New Bayesian Approach to Global Optimization on Parametrized Surfaces in R3

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 propo...

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Bibliographic Details
Published in:Journal of optimization theory and applications 2024-09, Vol.202 (3), p.1077-1100
Main Authors: Fradi, Anis, Samir, Chafik, Adouani, Ines
Format: Article
Language:English
Subjects:
Applications of Mathematics
Bayesian analysis
Calculus of Variations and Optimal Control
Optimization
Clustering
Engineering
Gaussian process
Global optimization
Mathematics
Mathematics and Statistics
Monte Carlo simulation
Operations Research/Decision Theory
Optimization
Parameterization
Riemann manifold
Theory of Computation
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Summary: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.
ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-024-02473-8