Using Julia to solve semidefinite programming problem that has vector solutions

Specific Domains Optimization (Mathematical)
5

Your objective is a matrix. You probably want to use convert it to a scalar using sum(X) or LinearAlgebra.tr(X).

There are also some issues with your constraints. (You need to use vectorized algebra: https://jump.dev/JuMP.jl/dev/constraints/#Vectorized-constraints).

Here are some PSD examples that might be helpful:
https://jump.dev/JuMP.jl/dev/examples/cluster/
https://jump.dev/JuMP.jl/dev/examples/min_distortion/

I would encourage you to re-read the PSA I linked. Instead of posting screenshots, post code that people can copy-paste. You should also provide all data needed to run the code.

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