AFAIK there is no option within REST API to be able to run all the tasks assigned to schedule in one go (ie same as selecting a schedule and RUN NOW)
However, you can Query Schedules for a specific Schedule ID,
and the Query Extract Refresh Tasks for that Schedule ID
and then run each of the extract refresh tasks (Run Extract Refresh Task)
Hope this helps
Thanks Glen, so... in spending many an hour, I was able to create the equivalent function to the "run schedule" using API 2.6 by:
1) SIGNIN (get auth token, site id)
2) Get Extract Refresh Tasks: extractRefreshes (note the plural as this returns 'em all)
3) grab returned xml matching where schedule name = "what I'm looking for" and pull it's associated extract refresh id (not schedule id): call this an "item"
4) Run Extract Refresh Task: for all items returned, execute a run Extract refresh task ...extractRefreshes/runNow (make sure your content-type header is set to "application/xml" or json...)
thanks for your help!