Is it possible to optimize over the following operator relative entropy cone natively in Julia:
\text{cl}\{(A, B, C)\in H^n_+ \times H^n_+ \times H^n: C \succeq - A^{1/2} \log(A^{-1/2} B A^{-1/2}) A^{1/2}\}
where cl stands for the closure, H^n is the space of n\times n Hermitian matrices, H^n_+ is the space of n\times n PSD Hermitian matrices.
Context
A previous topic raised a similar question. I’m seeking the latest information on whether this can now be done directly in Julia.
Hypatia.jl implements EpiTrRelEntropyTri, which seems to bound the trace of the matrix operator relative entropy of A and B, rather than directly constraining the three matrices A,B,C.
I don’t think there has been any progress. You’re still limited to the trace. But I’m not an expert in this area, so someone might come along to correct me. Let me know if you need an example using the trace. You could use Hypatia via JuMP, or you could use Convex.jl.
Hi odow. Thank you for the information.
I’m new to this field and have only used frameworks and solvers as a user, never contributed code or developed one. Maybe I could try customizing this cone later.
Is implementing this cone a good choice for a beginner? (I’m unfamiliar with the theory part and those self-concordant barrier function stuff, so I don’t know how hard it is.)
Are there beginner examples for customizing a cone?
