A general approach to solving hard problems is to solve a sequence of related, but much easier problems. Sequential approximation methods such as Newton's method are exactly of this type. In this talk we discuss such approach to solving certain constrained optimization problems, but where the easier problems are obtained by reversing the roles of the objective and the constraints. That is, we flip-flop the objective and the constraints. This idea was pioneered by Ewout van den Berg and Michael Friedlander in a pair of papers appearing in 2008 and 2011. We review this work and then study the question of just have far these ideas can be taken.