How to start a process out of Web Dynpro?
Once a process is deployed it exposes itself as a web service (so called 'web service provisioning'). Thus you could import this web service model into the Web Dynpro project and execute it like any other web service. As a result a new process instance will be started off with each successful web service request.
More Information: https://help.sap.com/saphelp_nwce711/helpdata/en/62/a6d7ac03994e0796c6b949c8952547/frameset.htm
Starting with 7.30 one has also the possibility to make use of the BPM Public API.
More Information: http://help.sap.com/saphelp_nw73/helpdata/en/9a/eebbdf59b94c3c82af598db638b0d0/frameset.htm