Please use the dedicated YALMIP Google groups forum instead
Answer: You basically cannot. Inverse operator is a horrible operator, and YALMIP is mainly about structured optimization. You should primarily try to look at your model, and come up with a clever linearizing variable change. The only way otherwise is to introduce a new variable and add the constraint X*Y==I (which of course will lead to a nasty nonconvex program which you most likely cannot solve anyway)