SOC-monotone and SOC-convex functions vs. matrix-monotone and matrix-convex functions

作者：Pan, Shaohua; Chiang, Yungyen; Chen, Jein-Shan^*

来源：Linear Algebra and Its Applications, 2012, 437(5): 1264-1284.

DOI：10.1016/j.laa.2012.04.030

• Hilbert space
• Second-order cone
• SOC-monotonicity
• SOC-convexity

The SOC-monotone respectively, SOC-convex function) is a scalar valued function that induces a map to preserve the monotone order (respectively, the convex order), when imposed on the spectral factorization of vectors associated with second-order cones (SOCs) in general Hilbert spaces. In this paper, we provide the sufficient and necessary characterizations for the two classes of functions, and particularly establish that the set of continuous SOC-monotone (respectively, SOC-convex) functions coincides with that of continuous matrix monotone (respectively, matrix convex) functions of order 2.

• 出版日期2012-9-1
• 单位华南理工大学; 中山大学