Are you aware of a fast solver (open source or commercial) for convex NLPs that is faster than IPOPT? I'm interested in problems in the 50K+ variable range, both dense and sparse. Ideally, it would be a solver dedicated to solving convex NLPs.
Are you formulating your model with nonlinear expressions that just happen to be convex?
Or can you provide conic normal forms, maybe using a modeling tool based on displicined convex programming? In that case, some solvers might be able to exploit that! Disciplined geometric programming is another way to teach solvers how to exploit convexity in nonlinear situations.
MOSEK is a commercial solver in that field.
UPDATE: Added a reference to DCP.
You may want to try out the NLP solver Knitro, which, despite being commercial, is faster than Ipopt: http://plato.asu.edu/ftp/ampl-nlp.html