Before revision:  In summary, TA and the\textit{  Spherical-CHM provide a convenient geometric setting for efficient solution to large-scale CHM and related problems, such as computing all vertices of conv(S)\emph{ }\hspace{0pt}%DIFAUXCMD , called }\emph{ }\hspace{0pt}%DIFAUXCMD } .
After revision:  In summary, TA and the\textit{ Spherical-CHM provide a convenient geometric setting for efficient solution to large-scale CHM and related problems, such as computing all vertices of conv(S)\emph{ }\hspace{0pt}%DIFAUXCMD , called }\emph{AVTA^+ }\hspace{0pt}%DIFAUXCMD } .