The parametrization of laminated composite structures for design optimization is a challenging problem. Manufacturing requirements limit the freedom to tailor composite structures to meet demanding performance requirements. Often, these manufacturing requirements are modeled by limiting the allowable ply angles to a discrete set of values. This discrete problem is not, in its most natural form, amenable to gradient-based optimization. On the other hand, methods for nonlinear mixed-integer programming are almost inevitably computationally expensive, especially for large design spaces. In our work, we use laminate parametrizations that take into account the discrete nature of the ply angles. To avoid solving a large, nonlinear, mixed-integer program, we use relaxation methods where the original discrete problem is transformed into a continuous analogue of the original problem. We then obtain solutions to the modified problem using gradient-based optimization.