Totally new to optimization. Is there an easy-to-use solver, package, (free) software for solving nonlinear semidefinite optimization problems?
If you use Python, I have found calling the
scs solver through
cvxpy to be very effective for semidefinite programming. The
scs solver uses ADMM as opposed to the interior point methods that are typically used for SDPs, with the result that it scales to larger problems but has a harder time achieving extremely high numerical accuracy. I haven't found this to be a limitation in my use cases.
Edit: Mark Stone suggests in the comments that this question is meant to address nonconvex problems as well, in which case these tools are inappropriate. I understood this question to mean that you had a (hopefully convex) problem over semidefinite matrices but with an objective that was nonlinear (i.e. the problem is not in the standard form required by SDP solvers). In this case these tools are worth a look, because
cvxpy converts the problem to standard form automatically. Some of these conversions can be tricky if you're not used to them, so it's helpful to have an automated tool.