"invite problems" is correct and can be used in written English.
For example you might say, "When you fail to plan ahead, you invite problems later on."
To shut out their concerns is to invite problems.
Andi Mallarangeng, a political scientist, said the inclusiveness of Mrs. Megawati's cabinet could invite problems.
Until politics is removed from the process, any government contract with private industry will invite problems.
But it could invite problems with a rigorously-minded referee.
For example, "I realise that you may have concerns over whether the idea of having water fountains around school may invite problems with people misusing them.
He said the hotel acts to ensure that there is no loitering in the parking lot and that it did not invite problem guests.
It is now clear that the way the OBR was established invited problems.
Mr. Carter invites problems, however, when he folds pungently contemporary elements into his score.
The Yankees are promoting Dwight Gooden to pitch today, even though some officials think the move invites problems in the event Gooden bombs.
Mr. Benjamin invites problems for himself in assigning the other role to a high soprano who is taken repeatedly into the stratosphere of her range, making it almost impossible to project text clearly, though the intense Ms. Komsi tried valiantly to do so.
Downgrading an employee's evaluation for work absences resulting from medical conditions just invites problems.
