You start AnyConnect on Centos 7 using the shortcut and the application flashes on the screen and disappears. So you try running it from the bash prompt and you get:

[user@mymachine ~]$ /opt/cisco/anyconnect/bin/vpnui
/opt/cisco/anyconnect/bin/vpnui: error while loading shared libraries: libpangox-1.0.so.0: cannot open shared object file: No such file or directory

The problem is that there has been changes in the pangox package. Execute:

yum -y install pangox-compat

and problem solved.

For more details see this article.