My optimisation problem has convex multivariate constraints with matrix operations: inverse and determinant. The matrices are symmetric PSD from dim 2x2 up to 10x10. I’ve solved the continuous case in JuMP and Ipopt, with userdefined multivariate constraints and analytical derivatives. This worked extremely well.
There’s been less luck with the integer case. What I’ve tried:

Define @NLconstraints in JuMP => The det and inv weren’t recognised

Use Pavito.jl and Ipopt with CbcSolver or CplexSolver => Requires Hessians, which isn’t possible in JuMP for multivariate userdefined functions, even though Ipopt doesn’t require exact Hessians

Juniper, POD, AmplNLWriter => No userdefined multivariate functions (to the best of my knowledge)

Convex.jl and SCS + Pajarito => some luck with the det, but slow convergence and inexact solutions, like 0.2039 for an Int x >= 0. Also, inv isn’t really allowed.
I’d very much appreciate any suggestions and recommendations of library tools, ideally open source. Many thanks!