What is the best solver for semidefinite programming in terms of speed and reliability?
I’m afraid there is no one right answer. In my experience, when all three produce good results, MOSEK 7 is faster than SeDuMI, which is in turn faster than SDTP3. (MOSEK 6 and earlier do not do SDP). But no one solver produces good results for every model. You will have to try them all to be sure.