A method for the design of displacement amplifying compliant mechanisms for piezoelectric actuators is developed using a topology optimization approach. The overall stroke amplification or geometric advantage of the mechanism, and the overall mechanical efficiency of the mechanism are considered as objective functions. The maximization of these objective functions is accomplished using two different solution methods, Sequential Linear Programming and an Optimality Criteria method. The focus of this paper is on the underlying topology optimization problem formulations and the solution methods. Design examples are presented which illustrate the method, with comparisons of the computation time and mechanism performance for the two formulations and solution methods. A procedure has also been developed to automatically convert the topology optimization results to a solid CAD model. A prototype design has been fabricated to serve as proof of concept.