Incremental Gradient Method for Karcher Mean on Symmetric Cones

Sangho Kum () and Sangwoon Yun ()
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Sangho Kum: Chungbuk National University
Sangwoon Yun: Sungkyunkwan University

Journal of Optimization Theory and Applications, 2017, vol. 172, issue 1, No 8, 155 pages

Abstract: 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.

Keywords: Karcher mean; Incremental gradient method; Symmetric cone; 65K05; 90C25 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10957-016-1000-4

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