The entire reason ISO dates were invented was to solve this problem and get rid of the ambiguity when writing dates.
The ISO date format makes sense. When you write a number, the most significant portion is on the left. It's the same with ISO dates; the year is the most significant part so it's on the left.
ISO dates also sort correctly without additional fiddling. They really are the answer to all the world's date-writing problems!
Now if I could only get the USA to switch to the metric system. It would be nirvana!