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.
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Acknowledgments
The first author was supported by Basic Science Research Program through NRF Grant No. NRF-2014R1A1A2056635. The second author was supported by Science Research Center Program through NRF funded by the Ministry of Science, ICT & Future Planning (No. NRF-2016R1A5A1008055).
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Communicated by Alexandre Cabot.
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Kum, S., Yun, S. Incremental Gradient Method for Karcher Mean on Symmetric Cones. J Optim Theory Appl 172, 141–155 (2017). https://doi.org/10.1007/s10957-016-1000-4
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DOI: https://doi.org/10.1007/s10957-016-1000-4