Using a relative path via './' or '../' will by default look from where you launched Nuke from. However if you first set the 'project directory' to be where the script is saved (via the 'Script Directory' button in Project Settings) it will look there instead.
This problem is limited to Windows when using '../' in the Write node filename and only if a project directory is set up in the Project Settings.
Using './' to use the relative directory works correctly but using '../' to use the parent directory causes a 'No backslashes allowed in filename' error when rendering. The error seems to come from the fact that the ellipsis is returning a file string with backslashes. For example evaluating the node returns something like this: C:/Users/USERNAME/Documents/NukeScripts\test.jpg
Furthermore this works correctly on CentOS and OSX. This also works on Windows if you write out to EXR.
Customer reported version
10.0v4
Steps to reproduce
1) Create a Checkerboard node
2) Attach a write node to it
3) Save the script
4) Open Project Settings (S)
5) Press 'Script Directory' to automatically point 'project directory' to the location of the saved script
6) On the Write node, type in './' followed by the filename (e.g. ./test.jpg)
7) Rendering this, will work
8) On the Write node, type in '../' followed by the filename (e.g. ../test.jpg)
9) Rendering this, will cause the error message: 'No backslashes allowed in filename'
10) Change the file type to EXR and try again, now it works
11) Repeat steps but do not set a project directory, it should now work normally
12) Try on OSX or Linux, it should work correctly
Reproduced by support Windows 10 - 12.1v1
Windows 10 - 12.0v1
Windows 10 - 11.0v1
Windows 10 - 10.0v4
Windows 10 - 10.0v1
Windows 10 - 9.0v9
Windows 10 - 8.0v7
Windows 10 - 8.0v1
Expected behaviour
To be able to write out to a relative path using '../' after setting a project directory
Actual behaviour
Setting a project directory causes the '../' relative path to fail on Windows