  We address the slow convergence and poor stability of quasi-newton sequential
quadratic programming (SQP) methods that is observed when solving experimental
design problems, in particular when they are large. Our findings suggest that
this behavior is due to the fact that these problems often have bad absolute
condition numbers. To shed light onto the structure of the problem close to the
solution, we formulate a model problem (based on the $A$-criterion), that is
defined in terms of a given initial design that is to be improved. We prove
that the absolute condition number of the model problem grows without bounds as
the quality of the initial design improves. Additionally, we devise a
preconditioner that ensures that the condition number will instead stay
uniformly bounded. Using numerical experiments, we study the effect of this
reformulation on relevant cases of the general problem, and find that it leads
to significant improvements in stability and convergence behavior.
