According to perlopentut, "You don't have to accept the STDIN and STDOUT you were given. You are welcome to reopen them if you'd like."

Then the example given, modified to affect STDERR.....

open( STDERR, ">errors.log") or die "Cannot open error log.\n$!";
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The tutorial also suggests that that it can be a clever thing to do to close the STD... filehandle on exit from the program, to force a flush.

END { close STDERR or die "Can't close STDERR.\n$!" }
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In your case, you simply want to redirect STDERR to the OUTFILE file handle. Also listed in the tutorial, you may do this:

open (STDERR, ">>&OUTFILE") or die "Can't redirect STDERR.\n$!";
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Hope this helps!