First off, you need to obtain the Pulse Secure client as a deb file from your network administrator. I have version 8.2R5.
For some reason the client does not list any dependencies when installing so you must install the needed (32 bit) libraries by hand (PulseClient.sh does not work without changes):
It is also necessary to include Pulse’s libraries in ld’s search patch (LD_LIBRARY_PATH). This is done by running this:
$ sudo ldconfig
The above instructions work for Ubuntu 16.04. 16.10, 17.04 and 17.10. In 17.04 and 17.10 you also need to install net-utils to get ifconfig