Does ProxSDP assume decomposition of X...?

[bcdandurand]

That is, instead of assuming one PSD constraint X in PSDCone(), we can have X_1 in PSDCone(), X_2 in PSDCone(), etc. Is this how ProxSDP is implemented? Or does it assume one matrix block X in PSDCone()?

I expect this question to be related to the issue:
Chordal decomposition issue

[bcdandurand]

If I understand the code in MOI_wrapper.jl correctly, the possibility of having more than one conic constraint (linear, SOC, and SDP) is allowed for.

[mariohsouto]

Yes, you can have multiple p.s.d. variables in your formulation. So if you have some way to decompose your problem into multiple smaller p.s.d. cones you should try it out.