My pleasure.
See this thread: Bottleneck of JuMP In a nutshell, there are two related problems: the first is that JuMP solves the primal problem by default, and YALMIP the dual. Here the dual happens to be more efficient. The second problem is a bug in Dualization.jl when dualising problems that use a non-native cone (here the complex PSD cone). There is a PR to fix it though: [breaking] change DualOptimizer to not add bridges by default - Pull Request #209 - jump-dev/Dualization.jl - GitHub