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Incremental Gradient Method for Karcher Mean on Symmetric Cones

Author

Listed:
  • Sangho Kum

    (Chungbuk National University)

  • Sangwoon Yun

    (Sungkyunkwan University)

Abstract

In this paper, we deal with the minimization problem for computing Karcher mean on a symmetric cone. The objective of this minimization problem consists of the sum of squares of the Riemannian distances with many given points in a symmetric cone. Moreover, the problem can be reduced to a bound-constrained minimization problem. These motivate us to adapt an incremental gradient method. So we propose an incremental gradient method and establish its global convergence properties exploiting the Lipschitz continuity of the gradient of the Riemannian distance function.

Suggested Citation

  • Sangho Kum & Sangwoon Yun, 2017. "Incremental Gradient Method for Karcher Mean on Symmetric Cones," Journal of Optimization Theory and Applications, Springer, vol. 172(1), pages 141-155, January.
    • Handle: RePEc:spr:joptap:v:172:y:2017:i:1:d:10.1007_s10957-016-1000-4
    DOI: 10.1007/s10957-016-1000-4
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    References listed on IDEAS

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    1. Defeng Sun & Jie Sun, 2008. "Löwner's Operator and Spectral Functions in Euclidean Jordan Algebras," Mathematics of Operations Research, INFORMS, vol. 33(2), pages 421-445, May.
    2. Sangho Kum & Yongdo Lim, 2010. "Penalized complementarity functions on symmetric cones," Journal of Global Optimization, Springer, vol. 46(3), pages 475-485, March.
    3. Paul Tseng & Sangwoon Yun, 2014. "Incrementally Updated Gradient Methods for Constrained and Regularized Optimization," Journal of Optimization Theory and Applications, Springer, vol. 160(3), pages 832-853, March.
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    Cited by:

    1. Glaydston Carvalho Bento & Sandro Dimy Barbosa Bitar & João Xavier Cruz Neto & Paulo Roberto Oliveira & João Carlos Oliveira Souza, 2019. "Computing Riemannian Center of Mass on Hadamard Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 183(3), pages 977-992, December.

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