We consider semidefinite programs, where all the matrices defining the problem commute. We show that in this case the semidefinite program can be solved through an ordinary linear program. As an application, we consider the max-cut problem, where the underlying graph arises from an association scheme.
Goemans, M. X., & Rendl, F. (1999). Semidefinite programs and association schemes (CORE Discussion Papers 1999/62). https://hdl.handle.net/2078.5/128165