SQP (Sequential Quadratic Programming) uses second-order information. If you have an AMPL mode, you can try out filterSQP on the NEOS server.
Convergence to a point of local infeasibility (= a minimum of constraint violation) is unfortunate, but a very good feature that is part of robust codes. You can try providing a different initial point.
My C++ solver Uno doesn’t have bindings to other languages yet, but it’s on my To-Do list 