A REMARK ON MULTI-DIMENSIONAL ANDO-HIAI LOG MAJORIZATION ON SYMMETRIC CONES

被引:0
|
作者
Kum, Sangho [1 ]
Lee, Hosoo [2 ]
机构
[1] Chungbuk Natl Univ, Dept Math Educ, Cheongju 28644, South Korea
[2] Jeju Natl Univ, Elementary Educ Res Inst, Jeju 63294, South Korea
关键词
Symmetric cone; second order cone; log majorization; Karcher mean;
D O I
暂无
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Recently, Bhatia et al. [3] established a multivariable extension of the Ando-Hiai log majorization theorem in terms of the Karcher mean on the cone P-n of positive definite matrices. As is well-known, P-n is one of the two representative examples of a symmetric cone in optimization fields. The other counterpart of P-n is the second-order cone (or Lorentz cone). It is of rank 2. In this work, we present the corresponding multivariable Ando-Hiai log majorization theorem with respect to the Karcher mean on the symmetric cone of rank 2 including the second-order cone. In addition, the case of rank 3 is treated.
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页码:1285 / 1295
页数:11
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