Computing Riemannian Center of Mass on Hadamard Manifolds

Glaydston Carvalho Bento (), Sandro Dimy Barbosa Bitar (), João Xavier Cruz Neto (), Paulo Roberto Oliveira () and João Carlos Oliveira Souza ()
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Glaydston Carvalho Bento: Universidade Federal de Goiás
Sandro Dimy Barbosa Bitar: Universidade Federal do Amazonas
João Xavier Cruz Neto: Universidade Federal do Piauí
Paulo Roberto Oliveira: Universidade Federal do Rio de Janeiro
João Carlos Oliveira Souza: Universidade Federal do Piauí

Journal of Optimization Theory and Applications, 2019, vol. 183, issue 3, No 10, 977-992

Abstract: Abstract In this paper, we perform the steepest descent method for computing Riemannian center of mass on Hadamard manifolds. To this end, we extend convergence of the method to the Hadamard setting for continuously differentiable (possible nonconvex) functions which satisfy the Kurdyka–Łojasiewicz property. Some numerical experiments computing $$L^1$$ L 1 and $$L^2$$ L 2 center of mass in the context of positive definite symmetric matrices are presented using two different stepsize rules.

Keywords: Riemannian center of mass; Steepest descent method; Kurdyka–Łojasiewicz property; Hadamard manifolds; Nonconvex optimization; 49J52; 65K05; 90C26; 58C99 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-019-01580-1

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